{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Fitting Global Warming\n",
    "\n",
    "It is well established that [global average temperatures have been rising](https://en.wikipedia.org/wiki/Climate_change) for many decades, and there is a [broad scientific consensus](https://www.ipcc.ch/) that this change is primarily due to human activity.\n",
    "\n",
    "But over short timescales, the random year-to-year variations in temperature are large, making it harder for humans to notice the long-term trend.\n",
    "\n",
    "How do we extract *average trends* from noisy data?  Linear algebra!"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Global temperature data 1973–2022:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The following is data on the change (°C) in [average global temperature](https://en.wikipedia.org/wiki/Global_temperature_record) (compared to the 1901–2000 average) since 1973 (the year Prof. Johnson was born), from the [National Centers for Environmental Information](https://www.ncdc.noaa.gov/cag/global/time-series/globe/land_ocean/1/1/1973-2022):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "year = [1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022]\n",
    "ΔT = [0.28, -0.19, 0.11, -0.02, 0.13, 0.16, 0.15, 0.33, 0.51, 0.14, 0.53, 0.3, 0.22, 0.31, 0.32, 0.56, 0.17, 0.36, 0.43, 0.46, 0.36, 0.27, 0.56, 0.25, 0.34, 0.6, 0.51, 0.34, 0.47, 0.71, 0.72, 0.61, 0.65, 0.5, 0.92, 0.27, 0.6, 0.73, 0.46, 0.44, 0.62, 0.69, 0.83, 1.12, 0.98, 0.75, 0.94, 1.14, 0.78, 0.89];"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "using PyPlot\n",
    "plot(year, ΔT, \"r.-\")\n",
    "xlabel(\"year\")\n",
    "ylabel(\"ΔT (°C) vs. 1901–2000 baseline\")\n",
    "title(\"Global average temperature change\")"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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6wc/PD8eOHTM7JFSW4n/RK7R4v2otXrwY48eP1//sTp06hW3btmHw4MEAZDhISEjA3r17S3xoq6HT6Ur8DH766SecPXsW9erV099n6dwAQO3atbF06VLk5eXpj8vKysK2bdsQGhpaZhvsfS89evTQ/65aM1RWFmvPibXatWuHwMBALFmyxCTs/f777zh16pRJGOrduzemTZuGqlWrIj4+3ub3QO6BYYg8wh133IFPP/0Uzz77LFq1aoWnnnoKt912G3x8fJCeno7vvvsOAEr9D71BgwZ46qmn8PHHH8PHxwc9evTAyZMn8dprryE2Nhbjxo0zOb5q1ap4+umncfr0adSvXx+rV6/G3Llz8fTTT6NWrVoAgF69emHGjBkYOHAgnnrqKWRlZeG9996zeS2WDh06oEqVKhg5ciQmTZoEf39/LFq0SD/kUlzDhg2RmJiI6dOn48yZM5gzZ47J9ytWrIiPP/4YQ4YMwaVLl/DQQw8hIiICFy5cwN69e3HhwgV8/vnnpbYpNDQUd911F959911Uq1YNtWvXxubNm5GSklLir++JEydi1apVuPvuuzFx4kQEBwdj1qxZ+jodpTegdu3amDp1KiZOnIjjx4+je/fuqFKlCs6fP48///wTISEhmDJlisU2KauDz5kzB5UqVUJQUBDi4+NRtWpVu9+vWpmZmbj//vvx5JNPIjs7G5MmTUJQUBAmTJigP2b27Nno0aMHunXrhscffxw1a9bEpUuXcPDgQezatatEWDSnd+/eWLBgARo2bIhmzZph586dePfdd0v0ciqrsy9atAiNGjVCxYoVER0djejoaAwaNAizZ8/GY489hieffBJZWVl45513rApCWryXRx55BF988QVGjhyJQ4cOoXPnzigqKsIff/yBRo0a4eGHH7a6HWrOibWUpRWmT5+OKlWq4P7770daWhqmTJmCGjVqmPRmjR07Ft999x3uuusujBs3Ds2aNUNRURFOnz6NdevW4bnnnkO7du1sage5gKsruInU2LNnjxg6dKiIj48XgYGBIigoSNSrV08MHjxY/PLLLybHmptaX1hYKN5++21Rv3594e/vL6pVqyYee+wx/dRjRVJSkrjtttvEpk2bRJs2bURgYKCoUaOGeOWVV0rMopk/f75o0KCBCAwMFHXq1BHTp08XKSkpJaaSWzubbNu2bSIxMVFUqFBBVK9eXQwfPlzs2rXL4gyhOXPmCAAiODhYZGdnm33OzZs3i169eonw8HDh7+8vatasKXr16iWWLl1a4nwZzwRTpKWliQcffFBUqVJFVKpUSXTv3l38/fffIi4uTgwZMsTk2F9//VW0a9dOBAYGiqioKPHCCy+It99+WwAQV65cMTn2+++/F507dxahoaEiMDBQxMXFiYceeshkCrwlM2fOFPHx8cLX17fEubHn/Q4ZMkSEhISUeD3ld0KhzFD66quvxJgxY0T16tVFYGCg6Nixo9ixY0eJx+/du1f0799fRERECH9/fxEVFSW6dOkiZs2apT9GmU1WfIaSEEJcvnxZDBs2TERERIgKFSqIO++8U/z6669mf68WL14sGjZsKPz9/QUAMWnSJP33vvzyS9GoUSMRFBQkGjduLJYsWWJxNtm7775boh3WvhdLbty4IV5//XWRkJAgAgICRNWqVUWXLl3Etm3b9MfAzBIWQogSv2/WnhPlZ2X88zd+n8a/O0VFReLNN98UMTExIiAgQDRr1kz8+OOPonnz5uL+++83efy1a9fEq6++Kho0aCACAgJEWFiYaNq0qRg3bpzIyMgo81yQ+9AJYePKcEREVkpOTsbJkydx+PBhVzdFM5s2bULnzp2xdOnSUgu2yfOdOHECDRs2xKRJk/DKK6+4ujnkABwmIyJNjR8/Hi1btkRsbCwuXbqERYsWITU1FSkpKa5uGlGZ9u7di8WLF6NDhw4IDQ3FoUOH9EOJw4YNc3XzyEEYhohIU4WFhXj99deRkZEBnU6Hxo0b46uvvsJjjz3m6qYRlSkkJAQ7duxASkoKrly5grCwMHTq1AlvvfWW5jMRyX1wmIyIiIi8GlegJiIiIq/mUWFoy5Yt6NOnD6Kjo6HT6cpc2G758uW45557UL16dYSGhiIxMRFr1651TmOJiIjII3hUGMrNzUXz5s3xySefWHX8li1bcM8992D16tXYuXMnOnfujD59+mD37t0ObikRERF5Co+tGdLpdFixYgXuu+8+VY+77bbbMGDAALz++utWHV9UVIRz586hUqVKZpfIJyIiIvcjhMDVq1et2g/Pq2aTFRUV4erVqyU2ZizNuXPnEBsb68BWERERkaOcOXOmzFXJvSoMvf/++8jNzUX//v0tHpOXl4e8vDz9baXj7MyZM6qWrCciIiLXycnJQWxsLCpVqlTmsV4ThhYvXozJkyfjhx9+QEREhMXjpk+fbnZPpNDQUIYhIiIiD2NNiYtHFVDbasmSJRg2bBi+/fZbdO3atdRjJ0yYgOzsbP3XmTNnnNRKIiIicoVy3zO0ePFiPPHEE1i8eDF69epV5vGBgYE27zhOREREnsejwtC1a9dw9OhR/e0TJ05gz549CA8PR61atTBhwgScPXsWCxcuBCCD0ODBg/Hhhx+iffv2yMjIAAAEBwcjLCzMJe+BiIiI3ItHDZPt2LEDLVu2RMuWLQEYNoRUpsmnp6fj9OnT+uNnz56NgoICPPPMM6hRo4b+6z//+Y9L2k9ERETux2PXGXKWnJwchIWFITs7mwXUREREHkLN57dH9QwRERERaY1hiIiIiLwawxARERF5NYYhIiIi8moMQ0REROTVGIaIiIjIqzEMERERkTppacDGjfKyHGAYIiIiIuulpABxcUCXLvIyJcXVLbIbwxARERFZJy0NeOopoKhI3i4qAkaM8PgeIoYhIiIiss6RI4YgpCgsBIz2DfVEDENERERknYQEwKdYdPD1BerVc017NMIwRERE5M7cqVg5JgZ48EHDbR8fYPZseb8HYxgiIiJyV+5YrBwUZLg+fjwwbJjr2qIRhiEiIiJ35K7Fynv3Gq7n5rquHRpiGCIiInJH7lisnJ8PHDxouH3unOvaoiGGISIiInfkjsXK//4L3LpluM0wRERERA4TEwO8847pfR9/7NpiZWWILDRUXjIMERERkUMlJprerl/fNe1QKGGoa1d5mZFRcijPAzEMERERuauTJ01v//KLS5qht2+fvLznHkCnkzVMFy64tk0aYBgiIiJyV0oYqlhRXm7Y4LKmADD0DLVuDURGyuvlYKiMYYiIiMhdnTghL/v3l5d//QVkZ7umLefPA5mZsqj7ttuA6Gh5P8MQEREROYzSM3TXXXIWWVERsHmza9qi9AolJAAVKjAMERERkRMoYah2beDuu+V1Vw2VKWGoeXN5yTBEREREDlVUBJw6Ja/HxxvCkKuKqJXi6WbN5CXDEBERETlUerpc4NDPTwaPTp3k/X//Let3nK14z1CNGvKSYYiIiIgcQhkii42Vgah6dUMQ2bjRuW3JyzNsw8FhMiIiInIK43ohhauGyv79FygoACpXNqyAzTBEREREDqVMqzcOQ126yEtnF1EbD5HpdPK6EoYyM2VQ8mAMQ0RERO7IXM/QXXfJzVqPHy+5OrUjKWFIKZ4G5LCdr68s9M7MdF5bHIBhiIiIyB2ZC0OVKgFt28rrzuwdUmaSKfVCgAxCUVHyuocPlTEMERERuSMlDMXHm97v7LohIUrOJFOUk7ohhiEiIiJ3U1gInD4trxv3DAGmiy8K4fi2nD8vN2NVtuEwxjBEREREDlF8jSFj7dsDQUFARoZhursjKb1C9esDwcGm32MYIiIiIodQhshq1ZK1OcaCgoA775TXnTFUZq54WsEwRERERA5hblq9MWWKvTPCkLniaUU5WYWaYYiIiMjdmJtJZkypG9q0SdYXOZKl4mmAPUNERETkIGWFoVatgLAwIDsb2LXLce3Iy5OrTwMcJiMiIiInsjStXuHnByQlyeuOXG/o4EG5unSVKoZtOIwpYejCBSA/33HtcDCGISIiIndTVs8Q4Jz1hsxtw2GsalXA319eP3/ece1wMIYhIiIid1LaGkPGlCLqrVvlcJYjKMXT5obIALn2UDkoovaoMLRlyxb06dMH0dHR0Ol0+P7778t8zObNm9G6dWsEBQWhTp06mDVrluMbSkREZKtz5+TQlL+/IWiYc9ttQGQkcOMG8PvvjmlLacXTinJQN+RRYSg3NxfNmzfHJ598YtXxJ06cQM+ePdGxY0fs3r0br7zyCsaMGYPvvvvOwS0lIiKykTKt3twaQ8Z0OsdOsTfehsNSzxBQLsKQn6sboEaPHj3Qo0cPq4+fNWsWatWqhZkzZwIAGjVqhB07duC9997Dgw8+6KBWEhER2cGaeiFFly7A4sWyiHrqVG3bkZEBXLxofhsOY+UgDHlUz5Ba27dvR3Jyssl93bp1w44dO3Dr1i2zj8nLy0NOTo7JFxERkdOoCUNKEfUffwDXrmnbDqVXqEGDkttwGGMYcm8ZGRmIjIw0uS8yMhIFBQW4ePGi2cdMnz4dYWFh+q/Y2FhnNJWIiEgqa1q9sfh4GZoKCoAtW7RthzVDZADDkCfQFZsKKP63w2/x+xUTJkxAdna2/uvMmTMObyMREZGemp4hwHQXey2Vtg2HMc4mc29RUVHIyMgwuS8zMxN+fn6oWrWq2ccEBgYiNDTU5IuIiMhpbA1D338PpKVp1w5rZpIB7Blyd4mJiUhNTTW5b926dWjTpg38lUWiiIiI3EVBAaCMSFgbhtLT5eWxY0BcHJCSYn87bt4sfRsOY0oYunRJPs4DeVQYunbtGvbs2YM9e/YAkFPn9+zZg9P/W5xqwoQJGDx4sP74kSNH4tSpUxg/fjwOHjyI+fPnIyUlBc8//7wrmk9ERFS6s2etW2NIkZYGvPCC4XZRETBihP09RAcPysUfw8OBmjVLP7ZKFSAwUF4vNhrjKTwqDO3YsQMtW7ZEy5YtAQDjx49Hy5Yt8frrrwMA0tPT9cEIAOLj47F69Wps2rQJLVq0wBtvvIGPPvqI0+qJiMg9KUNkcXFySntZjhyRAchYYSFw9Kh97TAunrZQY6un03n8UJlHrTPUqVMnfQG0OQsWLChxX1JSEnY5ckdfIiIiraitF0pIkKHJOBD5+gL16tnXDmuLpxXR0XKxSA8NQx7VM0RERFSuqZlWD8id5OfMMe1Fmj3b/A7zalhbPK3w8J4hhiEiIiJ3obZnCACGDQN27jTcHjjQvjZYuw2HMYYhIiIi0oQtYQiQPThVqsjrhw/b14b0dCArSw63lbYNhzGGISIiItKErWFIpwMaNZLXlSnxtjLehiMoyLrHMAwRERGR3WxZY8hYw4by8uBB+9qhdogM8PhVqBmGiIiI3EFampwWHxAAREWpf7xWPUO//y4v1QQy9gwRERGR3dSuMVScFj1DKSnADz/I62+/bf1q1koYys4Grl+3/fVdhGGIiIjIHaidVl+c0jN06JDsYVIrLQ146inDbSGsX806NBSoUEFeV7YH8SAMQ0RERO7A1uJpRe3acluMvDzg1Cn1j7dnNWsPX4WaYYiIiMgd2BuGfH2B+vXldVuGyhISSm69oWY1a4YhIiIisou9YQiwr4g6JgZISjLc9vVVt5o1wxAREZGRtDRg40b7d0/3JidOyEt7wpC9RdR5efJy4kQZzoYNs/6xDENERET/k5IiZ0R16SIvrZ2R5M1u3TIER1f1DBUWGtYYevRR9fubMQwRERHBMCNJKcQtKrJ+RpI3S0uT5yowEIiMtP15jHuGhFD32CNH5LT4ChUMtUdqMAwRERHBvhlJ3sy4XsiWNYYU9evLIuhLl4CLF9U9dvduedm8uawXUsuDV6FmGCIiIu0kJJT8MFczI8lbaVE8Dchenbg4eV1t3ZAShlq2tO212TNEREQEWWcyZ47htk6nbkaSt9IqDAG21w3t2iUvbQ1DSs/QtWvA1au2PYeLMAwREZG2hg0DQkLk9aQkdTOSvJUWM8kUtswoE8L+nqFKleQX4HGrUNsVho4ePYq1a9fixo0bAAChtliLiIjKnxs3gNxceT0/37Vt8RSu7hk6c0bWGfn5AU2a2P7aaofK3GQJBpvCUFZWFrp27Yr69eujZ8+eSP9fAhw+fDiee+45TRtIREQeJjPTcD0723Xt8CRahiFbeoaUXqHGjeWMNlupCUNutASDTWFo3Lhx8PPzw+nTp1FB2ZgNwIABA7BmzRrNGkdERB7IOAzl5LiuHZ4iPx84e1Ze17Jn6NQpQw9dWewdIlNYG4bcbAkGm8LQunXr8PbbbyOmWEFcQkICTtmyORwREZUfDEPqKGsMBQXZt8aQolo1+QUAhw9b9xhnhyE3W4LBpjCUm5tr0iOkuHjxIgLt6V4jIiLPVzwMFf/QI1PGQ2TFN0q1ldqhMmeHITdbgsGmMHTXXXdh4cKF+ts6nQ5FRUV499130blzZ80aR0REHuj8ecN1IawfqvFWWtYLKdQUUWdlyQJqAGjRwr7XtTYMxcQADz9suK12U1iN+dnyoHfffRedOnXCjh07kJ+fjxdffBH//PMPLl26hN9++03rNhIRkScx7hkCZO+QMuWaStJyWr1CTc+Q0itUty4QGmrf66opoFbqpJ5+GnjlFZeuRWVTz1Djxo2xb98+tG3bFvfccw9yc3PxwAMPYPfu3ahbt67WbSQiIk9SPAxxRlnpXN0zpNUQGWC6JUdpy+1kZABbtsjrL7/s8kU5beoZAoCoqChMmTJFy7YQEVF5YK5niCxzRBhSeoYOHwYKCuT6QZYoYahVK/tfVwlDN27IEFy5svnjli+XYaldO6BWLftf1042h6ErV67gzz//RGZmJoqKFccNHjzY7oYREZGHYhhSxxFhKC5Ozk67eVM+f2mFyfZuw2GsQgUZgK5ckatQWwpDS5fKy4cesv81NWBTGFq1ahUeffRR5ObmolKlStAZVb/rdDqGISIib6YUUFesKPep4jCZZcZrDMXHa/e8Pj5AgwbA3r2ybshSGLp2zTD9XoswBMi6oStX5FCZMlxn7Px5wxCZm4Qhm2qGnnvuOTzxxBO4evUqrly5gsuXL+u/Ll26pHUbiYjIUxQVARcuyOsJCfKSPUOWnTkjh4uCg4Hq1bV9bmvqhvbtk69fo4Y2axwBZRdRr1ghf09uv13b3jA72BSGzp49izFjxphda4iIiLzY5cty8TxAzk4CGIZK44g1hhTWzCjTsnhaUVYYUobI+vXT7jXtZFMY6tatG3bs2KF1W4iIyNMp9UKVKxt6OjhMZpkjptUrrOkZcnYYyswENm2S191kiAywsWaoV69eeOGFF3DgwAE0bdoU/v7+Jt/v27evJo0jIiIPo4ShiAjDmjXsGbLMEcXTCiUMHTwoh8LM9Tw5OwwpQ2StW2tbI2Unm8LQk08+CQCYOnVqie/pdDoUKl2kRETkXZTi6chIQxhiz5BlBw7IS0uzruyhbHlx5YoMqcVrgm7dAv7+W153VhhatkxeutEQGWDjMFlRUZHFLwYhIiIvZtwzFBYmr7NnyLyUFNlTAgD/93/ytpaCggy9L+bqhg4ckLPZwsK07aWxFIYuXgQ2bpTX3WiIDLAxDBEREZnFYTLrpKUBTz1luC0EMGKEvF9LpRVRK0NkLVpoW7xtaRXqFStkcX3Llobiejdh9TDZRx99hKeeegpBQUH46KOPSj12zJgxdjeMiIg8kLkwxGGyko4ckbUzxgoLgaNHtd2aolEj4KefzBdRO6JeCDCEofx84NIloGpVedsNZ5EprA5DH3zwAR599FEEBQXhgw8+sHicTqdjGCIi8lYcJrNOQoLsjTHuOfH1LX2laFtY0zOkdRgKDJQBKCtL9g4p1zdskN/35DB0Qpn+V+w6ERGRnrkCaoahkmJigI4dDSsx+/oCs2drv2Gppen1RUXAnj3yuhZ7khUXHS0DUHo60LQp8P33suerRQvtA58GWDNERETa4TCZ9ZRtOKZNk1Pshw3T/jWUnqEzZ+TWG4pjx4CrV2WRtXKMlooXUbvZXmTFWd0zNH78eKufdMaMGTY1xhqfffYZ3n33XaSnp+O2227DzJkz0bFjR4vHL1q0CO+88w6OHDmCsLAwdO/eHe+99x6qKmOYRESkHXPDZNeuyV4BX1/XtcvdnDolA4mvLzB6NFCpkmNeJzxc/iwyM4FDh+T6PoBhiKxp09J3tLeVcRi6dAn45Rd52w2HyAAVYWi3cuLKoNN6OXEjS5YswdixY/HZZ5/hjjvuwOzZs9GjRw8cOHAAtWrVKnH81q1bMXjwYHzwwQfo06cPzp49i5EjR2L48OFYoUxnJCIibdy8aRgSi4iQO5grrl0zhCMy1M+0beu4IKRo2FCGoYMHS4YhreuFFMZh6PvvgYICoFkzoH59x7yenawOQxuVtQFcaMaMGRg2bBiGDx8OAJg5cybWrl2Lzz//HNOnTy9x/O+//47atWvrC7rj4+MxYsQIvPPOO05tNxGRV1A2aPX3l4sI6nRAQICcVZSdzTBkTOkpuftux79Wo0ayNsm4bsiZYej4cXndTXuFADtrho4ePYq1a9fixo0bAABhXBWvsfz8fOzcuRPJyckm9ycnJ2Pbtm1mH9OhQwekpaVh9erVEELg/PnzWLZsGXr16mXxdfLy8pCTk2PyRUREVlCKpyMiDOvWcEZZSUI4PwwBhhllQjgvDP3zD7B+vbzupvVCgI1hKCsrC3fffTfq16+Pnj17Ij09HQAwfPhwPPfcc5o2UHHx4kUUFhYisthy4pGRkcjIyDD7mA4dOmDRokUYMGAAAgICEBUVhcqVK+Pjjz+2+DrTp09HWFiY/is2NlbT90FEVG4Z1wspOKOspH//BTIyZPFy+/aOfz2lQFrpGUpPlz8rHx9ZM+QIShg6fFhu+9GkiWMKtTViUxgaN24c/P39cfr0aVQwGhMeMGAA1qxZo1njzClekySEsFindODAAYwZMwavv/46du7ciTVr1uDEiRMYOXKkxeefMGECsrOz9V9nzpzRtP1EROVWaWGIM8oMlF6hO++UgcjRlJ6hI0dk7Y7SK9SwoWldl5aUhRcVbjxEBti4Ueu6deuwdu1axBRbDyEhIQGnTp3SpGHFVatWDb6+viV6gTIzM0v0FimmT5+OO+64Ay+88AIAoFmzZggJCUHHjh3x5ptvokbxHxaAwMBABAYGav8GiIjKO3NhiMNkJSnF0126OOf1YmJk6Ll+XdbvOHqIDACiokxvu3kYsqlnKDc316RHSHHx4kWHBYmAgAC0bt0aqampJvenpqaiQ4cOZh9z/fp1+PiYvkXf/03tdGR9ExGRV+IwWdkKCw2blTqjXgiQw2HGK1E7IwwtXGh620Jtr7uwKQzdddddWGj0RnU6HYqKivDuu++ic+fOmjWuuPHjx2PevHmYP38+Dh48iHHjxuH06dP6Ya8JEyZg8ODB+uP79OmD5cuX4/PPP8fx48fx22+/YcyYMWjbti2ilfFMIiLShvHq0woOk5navRu4ckX2mDli5WdLjOuGHB2Gim9CCzhmE1oN2TRM9u6776JTp07YsWMH8vPz8eKLL+Kff/7BpUuX8Ntvv2ndRr0BAwYgKysLU6dORXp6Opo0aYLVq1cjLi4OAJCeno7Tp0/rj3/88cdx9epVfPLJJ3juuedQuXJldOnSBW+//bbD2khE5LU4TFY2ZYgsKckxix1aotQNbd8OKFtqtWjhmNdy1ia0GrLpJ9G4cWPs27cPn3/+OXx9fZGbm4sHHngAzzzzjNk6HC2NGjUKo0aNMvu9BQsWlLjv2WefxbPPPuvQNhEREThMZg1nTqk3pvQM/fyzvIyLk6tTO0JCghyaMw5EjtiEVkM2x9KoqChMmTJFy7YQEZEn42yy0uXnA7/+Kq87q3haofQM5efLS0cO0cXEAHPmyKExZRsWR2xCqyGbaobWrFmDrVu36m9/+umnaNGiBQYOHIjLly9r1jgiIvIQQnCYrCy//w7cuCFrqm67zbmvXa+e7K1ROLJ4GpCbzp48KYvFHbUJrYZsCkMvvPCCfmXm/fv3Y/z48ejZsyeOHz+uakNXIiIqJy5flmvYAOwZskQZIuvSxbBCt7MEBgJ16xpuO2NB4ZgYoFMnt+4RUtg0THbixAk0btwYAPDdd9+hT58+mDZtGnbt2oWePXtq2kAiIvIASq9QWJj84FWwZsjA2esLFWe8JM6wYXIIy817bJzFpp6hgIAAXL9+HQCwfv16/X5h4eHh3MuLiMgbmRsiAzhMprh2TQ6TAc4vngbktPZ9+wy3i4rcfrq7M9nUM3TnnXdi/PjxuOOOO/Dnn39iyZIlAIDDhw+XWJWaiIi8gKUwxGEy6ddf5TBifLz8crYjR2RdlzE3n+7uTDb1DH3yySfw8/PDsmXL8Pnnn6NmzZoAgJ9//hndu3fXtIFEROQBygpD3t4z5OohMmW6uzE3n+7uTDb1DNWqVQs//vhjifs/+OADuxtEREQeyNzq04BhmOz6ddkz4syFBt2Jq9YXUnjgdHdnsvu38saNG7h165bJfaHKXwJEROQdyuoZAmTvkKMW+ktLk0NBCQnu9wGflQXs2SOvO3DLqjINGwZ06yaHxurVc7/z5EI2b9Q6evRoREREoGLFiqhSpYrJFxEReRlLYcjfHwgOltcdNVSWkiJXVO7SRV6mpDjmdWy1aZOs17nttpK7uTubB013dyabwtCLL76IDRs24LPPPkNgYCDmzZuHKVOmIDo62mQDVyIicpK0NLnAnatmB1kKQ4Bj64aUTUGVrR/ccZaUq4fIqEw2haFVq1bhs88+w0MPPQQ/Pz907NgRr776KqZNm4ZFixZp3UYiIiqNO/SMWBOGHDGjrLRNQd2Fq4unqUw2haFLly4h/n9TA0NDQ3Hp0iUAcsr9li1btGsdERGZV1QE7N4NTJgADB/u+p4RSwXUgGPXGkpIKLmaszvNkjp7Fjh0SM7kSkpydWvIApsKqOvUqYOTJ08iLi4OjRs3xrfffou2bdti1apVqFy5ssZNJCLyYsaFwb6+wLp18is1FbhwwfxjnL1+TF6eodfH2cNkNWvKouysLHlbp3OvWVJKr1Dr1gA/H92WTWFo6NCh2Lt3L5KSkjBhwgT06tULH3/8MQoKCjBjxgyt20hE5J1SUkzrYYqrWBFITATWrzddUM/ZPSNKKPPzM/+B78hhssOHDUEIAPr2da8tJlgv5BFsCkPjxo3TX+/cuTMOHjyInTt3om7dumjevLlmjSMi8lrFC4MVzZoBffoAyclA+/ZAQIAMTU8+KQORK3pGlHqh6tVLLuwHOHaYbO1aeenvD9y6BWRkaP8athKCYchDaLL6VVxcHOLi4rR4KiIiAswXBgPAhx/KqdHGhg2TH7xPPimnbg8d6pQm6pVWPA04dphszRp52a8f8PXXwLFj2r+GrY4elaE2IADo0MHVraFS2FRADQC//PILevfujbp166JevXro3bs31q9fr2XbiIi8l9rtEx59VA6bpacDf/7p+PYZK614GnDcMNnNm3INHwAYNUpeXrzoPlt/KL1CHTqY7hhPbsfmvcm6d++OSpUq4T//+Q/GjBmD0NBQ9OzZE5988onWbSQi8j4xMYDxFkdlbZ8QHCyHzwBg6VLHt89YWT1Djhom+/VX4MYNIDpaBo5q1eT9x49r+zq2WrVKXrZp49p2UJlsCkPTp0/HBx98gMWLF2PMmDEYM2YMvv76a3zwwQeYNm2a1m0kIvJObdvKy6pVgZMnyy4MfugheblsWckdyh3JVcNkyhBZt26yVqpuXXnbHcLQ3LnA6tXy+owZ7rcqNpmwKQzl5OSY3Z0+OTkZOe7SPUlE5OkOHZKXzZpZVxDdowcQEgKcPg389Zdj22bM2jCk9TCZEoaUz6M6deSlq+uG0tKAkSMNt91xVWwyYVMY6tu3L1asWFHi/h9++AF9lG5aIiKyjxKGGjSw7vjgYKB3b3ndmUNlShiyVDPkiGGyM2eAAwdkXVXXrvI+d+kZOnzY/VfFJhNWzyb76KOP9NcbNWqEt956C5s2bUJiYiIA4Pfff8dvv/2G5557TvtWEhF5I7VhCJCzqpYskWHonXdKrs7sCEoBtTN7hpQp9e3ayUUXAffpGTp9uuR97rQqNpVgdRj6wLiQD0CVKlVw4MABHDhwQH9f5cqVMX/+fLz66qvatZCIyFvZEoZ69JAzl06dAnbudE7xritqhozrhRTu0DNUVATMnCmv63Sydqus4ndyOavD0IkTJxzZDiIiMmY8rKImDFWoAPTqJXuGli51fBgSwvmzyQoK5KrbgKFeCDD0DJ06JY/x02QpPXWWLgX27pUBcOtWuTp2vXoMQm7O5nWGiIjIgU6flnt+BQTInejV6NdPXi5d6vhZZdnZcuVnoOyeoZs3gfx8+1/zjz/k64aHm4a96GggMFAGoTNn7H8dtQoKgNdfl9efew5o2lQukMkg5PYYhoiI3JEyRFavnhxmUaNnT1lMfeIEsGuX9m0zpvQKhYYCQUHmj6lUyXBdi94hZYgsOdn03Pj4APHx8ror6oa++koWT1etCowd6/zXJ5sxDBERuSNb6oUUISFyqAyQaw45UlnF04AcrgoJkde1DEPG9UIKV9UN5eUBU6bI6xMmGHrDyCMwDBERuSN7whBgWIBR7VBZWhqwcaP1a+KUVS+k0GpG2YULsjAcMB+GXDWjbO5cWasUHW3YGoQ8BsMQEZE7sjcM9eolh62OHQP27LHuMSkpsj6pSxd5ac2qyWrDkL09Q6mpMtw1bw7UqFHy+67oGbp+HXjrLXn91VflECV5FJtK7Y8cOYJt27YhIyMDOp0OkZGR6NChAxISErRuHxGRd7I3DFWsKGuHli+XvUMtW5Z+fFoa8NRThsUClVWTu3UrvQDY2jCk1Yyy4qtOF+eKnqFPPgEyMoDatcveMoXckqowlJ2djcGDB2PVqlUICwtDREQEhBC4cOECcnJy0KdPHyxcuBChHCslIrLdtWvA2bPyuq1hCJCzypQw9NZbpS/AuH695VWTrQlDllafVmgxTFZUZFhs0dwQGWDoGTp2TPYgOXrRyexs4O235fUpU+TsP/I4qobJnn32WZw4cQLbt2/H5cuXcejQIRw+fBiXL1/Gtm3bcOLECTz77LOOaisRkXc4ckReVqtmWF3ZFr16yanmR48C+/ZZPu7MGVn0W5w1qyZbU0ANaDNMtnevDF8hIcAdd5g/RplNlpMDXLpk+2tZa8YM+TqNGgGPPur41yOHUBWGVq5ciblz56Jdu3YlvteuXTvMnj0bP/zwg2aNIyLySsoQWf369j1PpUpyRWrA8l5lWVmylyUjQ/buGPekWLNqsjOHyZQhsrvvttwDExwsi5gBxw+VXbwowxAATJ2qfgkEchuqC6h1pXQ5lvY9IiKykr31QsZKW4AxN1f2Hh08CNSsCfz5J/D77/J7Oh3Qv3/Zz+/M2WRl1QspnFVE/fbbckizZUvggQcc+1rkUKrCUJ8+ffDkk09ix44dJb63Y8cOjBw5En379tWscUREXknLMNS7txwqO3wY+Ptvw/23bsmg9McfQJUqwLp1QK1aQNu2cqhJCGDbtrKf31mzyXJyDO2xVC+kcEYR9Y4dwIcfyutvvSUXfCSPpeqn9/HHHyM6Ohpt27ZFeHg4GjZsiEaNGiE8PBzt2rVDjRo1THa3JyIiG2gZhkJDDeFBGSorKgKeeAL4+Wc5rPTTT0DjxobH3HWXvNy8ufTnzs8HLl+W18sqoLZ3mGzDBrndRUKCIexY4uieoZQUGRqVbUiUYnfyWKpmk1WuXBk///wzDh48iN9//x0ZGRkAgKioKCQmJqJhw4YOaSQRkdcQQvbiANqEIUD2AK1cKcPQlCnA888D//2vrHFZuhRITDQ9PikJ+PJLYMuW0p/3wgV56esre5dKY+8wmbVDZIBje4aUJQiMhxxHjpTt4h5kHsumdYYaNWqERo0aad0WIiJKT5d1KL6+hh4Oe/XpIwuO//1X1gj9/LO8f/58w7YdxpSeoT//BG7csLyIoDJEVr162cNE9gyTCaEuDDmyZ+jIEduWICC3pnqQUwiB1NRUTJkyBU8//TRGjRqFKVOmYP369RCO3h0ZwGeffYb4+HgEBQWhdevW+PXXX0s9Pi8vDxMnTkRcXBwCAwNRt25dzJ8/3+HtJCKyiTJEFh+v3Zo1YWFy6jdgCEL9+gGDB5s/vk4dOSPr1i1ZU2SJtfVCShsA28LQ4cNyq4uAANlrVRalZygtTe4ZpiVziwtbswQBuTVVYejs2bNo1aoVevTogRUrVuD48eM4evQoVqxYge7du6NNmzY468Cx0yVLlmDs2LGYOHEidu/ejY4dO6JHjx44ffq0xcf0798fv/zyC1JSUnDo0CEsXryYw3lEZJnavbm0ptW0emNpaSXXGVq+3PJ71OkMvUOlDZWpCUP2DJN98428bNvWsOFraapXlytwCwGcPKn+9UoTE2P6fn19rVuCgNyaqjA0atQohIeH48yZM9izZw/Wrl2LdevWYc+ePThz5gwqV66MZ555xlFtxYwZMzBs2DAMHz4cjRo1wsyZMxEbG4vPP//c7PFr1qzB5s2bsXr1anTt2hW1a9dG27Zt0aFDB4e1kYg8mC17c2lNy+JpxZEjJafVK0M7lqgJQ2UVTwO2D5OlpACTJ8vrv/1m3c9Ep3Nc3VB2tuF9f/+9DFvcgsPjqQpDv/zyC2bMmIEaZjbHq1GjBt577z2sX79es8YZy8/Px86dO5GcnGxyf3JyMrZZmP65cuVKtGnTBu+88w5q1qyJ+vXr4/nnn8eNGzcsvk5eXh5ycnJMvojIC1jam8vZPUSOCEMJCSVresoa2lHC0LZtctaYOdauPg0Yhsmys0sGM0uUn4lCCOt/Jo6qG9q1S17Wrg3cey97hMoJVWEoODgYl0pZ3vzy5csIdtBuvRcvXkRhYSEii/0FEhkZqZ/VVtzx48exdetW/P3331ixYgVmzpyJZcuWldp7NX36dISFhem/YmNjNX0fROSmSiuMdSZHhKGYGGDOHMMKydYM7TRuLLcDuXED2LnT/DG2DJPdumV9HY89PxNH9Qwp6+y1aaPt85JLqQpDDz/8MIYMGYJly5Yh22jcNzs7G8uWLcPQoUMxcOBAzRtprPgq10IIiytfFxUVQafTYdGiRWjbti169uyJGTNmYMGCBRZ7hyZMmIDs7Gz915kzZzR/D0TkhhISSm7q6ezC2Lw8Q42LlmEIkEM5J0/KeihrhnZ0OqBjR3nd0lCZmjBUsaLhurU97vb8TBzVM8QwVC6pCkPvv/8+evXqhUcffRTh4eEIDg5GcHAwwsPD8eijj6JXr1549913HdLQatWqwdfXt0QvUGZmZoneIkWNGjVQs2ZNhCnds5DLAgghkGahmzUwMBChoaEmX0TkBWJiDDOuAPkh7OzC2GPHZE9IpUpAVJT2zx8TA3TqZP17KqtuSE0Y8vWV7wuwvog6JsZ0SxA1xcrsGSIVVK0zFBAQgM8//xxvv/02duzYgfP/Gy+OiopC69atHRocAgIC0Lp1a6SmpuL+++/X35+amop7773X7GPuuOMOLF26FNeuXUPF//1VcvjwYfj4+CCG47xEVJxxj3FAgPP3mzIeInOHvR6VMLR1qxyeKr4RqZoCakAOlV29qq6IWvm/ul8/uSmqtf93G/cMCaHN+bx0ydDT1KqV/c9HbsOmzVRCQ0PRpUsXPPLII3jkkUfQuXNnp/SgjB8/HvPmzcP8+fNx8OBBjBs3DqdPn8bIkSMByCGuwUbrZgwcOBBVq1bF0KFDceDAAWzZsgUvvPACnnjiCYfVNhGRh8rPl2vZAEBsrByyWrjQuW1wxLR6ezRvLntzcnJKTs0XQl0BNWDbjDKlFz8xUV0vXVycLBq/cQOwUFeqmlI8Xbdu2Stuk0dRvQJ1bm4uvv76a2zbtg0ZGRnQ6XSIjIzEHXfcgUceeQQh1qwBYaMBAwYgKysLU6dORXp6Opo0aYLVq1cjLi4OAJCenm6y5lDFihWRmpqKZ599Fm3atEHVqlXRv39/vPnmmw5rIxF5qJMn5RBVhQrAyy8DzzwDzJoFjBnjvF4aRxRP28PXF7jzTrlQ45Ytcnd2RU6OYZZZ9erWPZ/xjDJrKWFIbW++v7/cePbkSdmbY2YWtGocIiu3VPUMHThwAPXr18eLL76Iy5cvo1atWoiJicHly5fxwgsvoEGDBjhw4ICj2gpArnV08uRJ5OXlYefOnbhL6cYFsGDBAmzatMnk+IYNGyI1NRXXr1/HmTNn8P7777NXiIhKUmYo1asHPPaYXNzv33+BMla515S7hSHAsOJz8U1blSGyihVlgLSGLT1DyiQWW2b2KkNlWtUNMQyVW6p6hp555hncdddd+PLLLxFQbJn4/Px8PP7443jmmWewceNGTRtJ5NXS0uQU44QE71zTxFnvX/nArFdPfmgPHAjMnSt7h4z+6HIodwxDxkXUxrU3aoqnFWq35CgsBM6dk9dt+dnXqQP88gvDEJVJVc/QH3/8gddee61EEAJkgfMrr7yCP0rbx4aI1HGHFZFdyZnv37hnCJCL+wHAd98Zdmd3pKwsWaALmN//ylVat5YbtWZlAQcPGu5XWzwNqN+SIzMTKCiQtT+2zK7Tcnr9xYuGmjLj4UIqF1SFoSpVquDIkSMWv3/06FFUYVEZkTbcZUVkV3H2+y8ehlq3lj0A+fnAggWOeU1jSq9QbKx1+285S0CALF4GTKfYqy2eBtQPkyk/6xo1AD/VJa7aTq9XFp6sX9/Qw0Xlhqow9OSTT2LIkCF47733sHfvXmRkZOD8+fPYu3cv3nvvPTzxxBMYofw1RUT2cZcVkV3F2e+/eBgCgP/NVMXs2SXbojV3HCJTmFtvyBnDZPbUCwHa9gxxiKxcUxW1J0+ejODgYMyYMQMvvviifuVnIQSioqLw8ssv48UXX3RIQ4m8jrL6rvE+Ts5eEdmVlP20jEOIo95/QQFw4oS8rnyAAsDDDwPjx8uehQ0bgK5dtX9thbtNqzdmrm7IljCkdpjM1plkCqVn6Px54No101Ww1WIYKtdUrzP00ksv4dy5czh27Bi2bt2KrVu34tixYzh37hyDEJGWYmJMP5jVrL5bHsTEAKNHG277+Dju/Z85I/fMCgw0ff6QEGDQIHl91iztX9eYO/cMtWsnp6qfPWsIjfaEIbXDZLb+zCtXBsLD5XWl3bZiGCrXbFp0EQDi4+ORmJiIxMRExMfHa9kmIlIof0GHhFi3n1R5YxwMJk1y3PtXhsjq1Cm5u7sy9P/990B6umNeH3DvMFShAtC2rbyuTLFXaobUFFCrHSazNwwB2tQNnT8v26LTsXi6nFIdhm7cuIGtW7eaXU/o5s2bWOjsFVuJyqvLlw2zmHJzgapVXdseV1A2LQXUrU2jlvG0+uKaNgU6dJD1SvPnO+b1CwoMgcwdwxBQsm7IGcNk9tYMAdrUDSnF0w0b2jfURm5LVRg6fPgwGjVqhLvuugtNmzZFp06dkG70l1J2djaGDh2qeSOJNJGWJnfs9pTZWIcPm95W/hL3JsZhyGh1ec2ZK542phRSz5kjQ5HWTp2Sw3RBQXLVZHekZRjytJ4hDpGVe6rC0EsvvYSmTZsiMzMThw4dQmhoKO644w6TLTCI3JInrtejDJsotNpfyZO4Sxh66CFZe3L6NLB2rfavr/yslaJxd9Shg2zb8ePy56KsiWTLbDJreoaKimSNEmBfGNKiZ4hhqNxT9a9u27ZtmDZtGqpVq4Z69eph5cqV6NGjBzp27IjjWkxdJHIET12vp3gYYs+Q416nrDAUHAwMGSKvO6KQ2p3rhRShoYZ6meXL5aWPj6FA2drnAGTPkPEsSXMuXJC9ZTqdffuKsWeIrKAqDN24cQN+xRa++vTTT9G3b18kJSXhcPFufSJ34Knr9Xh7z9C1a6YrP6eny53ktVZUZPigNJ69V5xSSP3TT4ZaFq2487R6Y8pQ2dKl8rJ6dTnL0VpKGCoslLvJl0Y5xzVqyJlstlJ+pidP2jbEee6c/N3z8QFatLC9HeTWVIWhhg0bYoeSkI18/PHHuPfee9G3b1/NGkakGWW9HmOesF6P8YrEgPeFIWXrg7AwWUsDGIZNtHTuHHDzplzhOC7O8nENGgCdO8vwNG+etm3whJ4hwLBp6++/y0s1Q2SALD5W/i2WNVSmRb0QANSsKVfRvnXLtt5g5TOvcWPrN6Qlj6MqDN1///1YvHix2e998skneOSRRyDK6vokUkOLoueYGKB5c8NtT1ivp7BQ9mgBhg8gbwtDyhBZfLyhqNgRQ2VKD2Ht2mVv+aD0Ds2aBaSmajfU6ilh6M47TW+rDUM6nfVF1FqFIV9f+bMFbKsbUmaScYisXFMVhiZMmIDVq1db/P5nn32GIkcvWU/eQ8uiZ6VnAQBWrnT/9XrOnJFDQoGBcsE7wHvDUO3ahjCk9BZpqbRp9cXdf7/s3cjMBJKTtSnGz8kxrF/k7mGoalWgSRPDbbVhCHB+GAIMQ2W21A2xXsgr2D1tYfHixcjNzdWiLUQGWhc9GwcJZRaMO1N6CurVk938AMMQ4NieIWvCUGamXPNJoUUxvtIDGBEhV0x2d0rdEGBbGLJ2RpkWawwplCJqtT1DQjAMeQm7w9CIESNw3htnuZBjaVn0LIRpkPj3X/va5gzGBbVRUfI6w5Drw9CRIyVnQdlbjO8pQ2QK4zBk3ONqLU/qGUpLkwHY1xdo1sz+dpDbsjsMsUaIHMLceiu2Fj3n5MgCWcXBg/a1zRmMPyCNw5A3/XtT9pJyVs2QNb9bWv5eKjwtDBn3gr3zjvphQleEIVt7hpReoSZN5PIKVG656epe5PViYgDj1cx1OtuLnov3qHhSz1CDBoa9n27edOyWFO7GuGdImeWldRgSQl0YiomRq1ArtNg81lOm1QMyoBhvyC2E+mFCa4bJhDA8pxbDZLb2DLF42mvYHYZ0xacsE2nFeA+gIUNsL3pWhnFDQuTlkSNyLyh3ZhyGKlQw/DXtLUNlV68CWVnyelycac+Qlr1jmZlyPSOdzjDjqCzDhgFjx8rr999vfzG+J/UMaTF8bU3P0IULQH6+/QsuKpTNxC9fll/WYr2Q1+AwGbkv4zWtrl61/XmUANGypQwWt27ZtzS/o+XmGv4qVj4gld4hb6nPU2aNVakiexKUnpfr17UtgFc+xGvVkjP3rHXPPfLy77/te/2iIsMedJ4QhrQYJrQmDCm//5GRco0ge4WEGIabrf23z+Jpr2J3GPr5559RU5ntQqSVggJg927DbaMNgVVTwlCNGnLXacC964aU2UXVqhm2OvC2ImrjITJAFuoqgVDLoTI1Q2TG2raVl4cOqetpKO7cORnw/PwMdS3uTBkmVFadtmXNLmuGybSsF1Ko3Zbj1CnZO+nvDzRtql07yC3ZHYbuvPNOBKr5i4rIGv/+Kz8kFFqEoagozwhD5oZNvD0MAY4polazxpCxatUMH65//WX76ys/6zp17NtywpmGDZM/n40b5aXaYUI1PUNa1Asp1G7YqvQKNW2qrteQPJKmBdQHDx5EHU/464bcn/IfkfIBeO6c7bUixmGoUSN53Z2LqM0V1HprGFJqPQDHhCFbe4YAw2KYf/xh++sr21oo781TxMQAnTrZ1nNjTRhS1hhyZc8Qi6e9iqZhKD8/H6ccsUIseR8lDPXuLS/z8oArV2x7LvYMeR5lWr2je4ZcGYZSUoDXXpPXf/nF/pWsPYWrhsls7RliGPIKZWzEY2r8+PGlfv+C8Q7TRPZQ/iq7805g8WJZl5GeLgtq1TIOQ8oU7X//lT1N7jgbkmHIecNkWoShP/9U/7ukrLCu9HYqU9S7dXPvPfO0oGaYzFU9Qyye9jqqwtCHH36IFi1aIFT5ZS7m2rVrmjSKvNytW8CePfJ6mzay8FkJQ40bq38+4zBUr56cDaPsBxUdrVmzNSGE+4ehtDRZ5J2Q4LgPbmeEoUuXDMXPtgzvt2gh63wuXJDtNR7SK0tpU9QZhhxbM3T6tOwdKu1nfvy47IkOCABuu027NpDbUhWGEhISMG7cODz22GNmv79nzx60bt1ak4aRFztwQC4wGBYm/wOrUUPeZ0sRdWGhXEsGkIEiMFA+55EjsnfI3cJQerpc98bX1/CfN+A+YSglxbBnnI+PnFmk9aa3OTmG6fNKTx6g/WatSq9QdLRcckGtoCAZiP76Sw6VqQlDyhR140Bk70rWnqKsYTLjBRe1DIY//mh4/oSE0n93lV6h5s21mdpPbk9VzVDr1q2xUxm+MEOn03HdIbKf8h9R69byA0NZdO3cOfXPlZUlA5FOB1SvLu9z57ohZc2Z+HjT/4SVMJSZKd+PK2i9ea4lStgJDzf0IgCGMJSeLmvI7GXPEJnC1rqhmBhDPRxg2xR1T2XcM2Tu8yIry7B9jlZ/rKSlyd9VRVGR/F229LvLITKvoyoMvf/++xirrLxqRvPmzVFUvOuXSC3jMAQY/kO0pWdI6UmpVs0wddmdZ5RZ2pqhenUZ6AoLDSszO9uSJdptnlsac0NkgDwHysagZ8/a/zq2Tqs3pqw3ZEsRtdJj+fzztk1R91RKGBJC9oIWpwSUiAjtprSbG5YsKgL69ZO9zsVxJpnXURWGoqKiEGfcbU3kCMX/I1J6hmwJQ8qKzUrPCuDePUOWtmbw95eBDnD+UJkQwKefmu5JpfDx0X5ox9y0ekCGQS3rhrTsGdq1S24fYa2sLFl4DQD/+Y939AgpKlQwLNporm7IEfVC5lbOBuTSBk2byl4i5f+XoiKGIS9k89T6U6dO4Y8//sCff/7J6fSknfx8YO9eeV2LMGRcPK3whJ4hc1szKO/BmVty5OcDTz8NjB4tPyTatTN8kAFyWwqtP8jNTatXuFsYSkiQMxzz8oD9+61/3Pr18nw2aeJdQQiQoba0ImpHrDFkbuXsN9+Ue8sVFQFz58rfg0mTgLVrZbsCA22bsEEeSXUY+uCDDxAbG4s6deogMTER7du3R506dRAbG4uZM2c6oInkVf7+W34AV6li6BnQIgwpWzkAhp6hs2fdbxf40sKQ8h6c1TN08SKQnCxrWXQ64O23ge3bZc/N1KnymP37ta9hsjRMBrhfGNLpbBsqW7tWXnbrZvtrezIlDJkronZE8TRQcuXsiROB5cuBX38F2reXK95PnQr07CmPz8sDvvxS2zaQ21IVht544w1MnjwZo0ePxs6dO3H27FmkpaVh586dGD16NCZPnow333zTUW0lb2BcuKis22JPAbW5nqHKlQ233al3KC/P0CtSWs+QI8NQWpr8sFi/Xn7Ib94MVKoErFwph8l0Ovkh9eKLMrCeOwds2KBtG5wRhnJyDDU7xrP2bKG2iFoIYM0aeb17d/te21MpM8pKGyZzRI+ZuZWz77wT2LYNmDWr5PGOmCBAbknV1Po5c+bgyy+/xH333Wdyf3R0NFq0aIH69etj9OjRePXVV7VsI3mT4sXTgCEM5ebK3esrVbL++cyFIUAOlWVkyDCk/GXvaseOyS77SpVKthdwfBgynjavqFNHBqHia60EBgIDBsgPkK++MuzirgVnhCGleLp6ddMZa7ZQG4b275e9nBUqyA9ib1TaMJkjaobKotOVnLQAeM/aT6SuZygrKwsNzP3F+j/169fHZXt2cCYyN6W1YkVDAFI7VGYpDLljEbUyrb5BA/OrGTsyDBWfNq/4/nvLi84NHiwvly+XQVUL2dmGhRDNTdbQKgxpMUSmULuDvdIr1KmTYXactyltmMwRNUPWMFdk7S1rP5G6MNS2bVu89dZbKCgoKPG9goICTJs2DW3d5a9s8jw3b8qaIaDkLA5b64ZK6xkC3GuYzNK0eoUjw5C5qcdA6dP427eXHxS5ucCKFdq0Q5mMUbWq+R5A4zBkz5pmWkyrV6jdwV6pF/LWITLA8jCZoxZctIa5ImtvWfuJ1A2Tffzxx0hOTkZERASSkpIQGRkJnU6HjIwMbNmyBYGBgUhNTXVUW6m8279fbsVRrVrJXbxr1JA9J+W5Z6i04mnAsWEoIUH2RhkHjLL+KtbpgMceAyZPBhYulNftpdRMWVrNWflgys2VvTDh4ba9jpY9Q4AcKjt+XA6VJSdbPu7aNVmwC3h3GLI0THb5MnDjhrxes6Zz2wTIIutu3eTvR716DEJeRFXPUNOmTXH48GG89dZbCA0NxYkTJ3D8+HGEhobirbfewr///ovbuI8L2cpc8bTCliLqvDzDtg6WeoaOHZMBzB24Mgzl5Zmec2v/KlYC0C+/2FbgXlxp9UIAEBwsF+MD7Bsqc0QYAgxrB1mycaP8fatTx7uHXywNkym9QsYLbDqbuSJrKvdU9QwBQKVKlfD000/j6aefdkR7yJuZK55W2DJMpswW8vcvudt9zZqyFunaNfnBqIQjV7I2DF26JMOLVqvzArJ3p6gISEqS1639q7huXeCOO4DffgO+/lqupmyPssIQIHsNMzNlGGrRwrbXcVQY+uOP0newV+qFunVTt8t9eWNpmMxV9ULk9WxadDE3NxdbtmzBkiVLsGzZMuzatctpe5J99tlniI+PR1BQEFq3bo1flS7nMvz222/w8/NDC1v/8yTHK20/IFu25FAWJ4yMLFkYqdMZhsrcoW4oK8tQn5OQYP6YKlUMW4ooQU8L//wDLFokr7//vvq/igcNkpdffWV/W6wNQ4DtG7Zev27YzkOrMFR8B3tLWC8kWRomc1W9EHk9VWGoqKgIL774IqpXr47OnTtj4MCB6N+/P9q0aYP4+HisWrXKUe0EACxZsgRjx47FxIkTsXv3bnTs2BE9evTA6TK6y7OzszF48GDcfffdDm0f2eHGDfmhDJgPQ7b0DFmqF1K4U92Q0isUGwuEhJg/xsfHMQsvvv667M144AHzvXJl6d9fbiq7b59h9XBbqQlDtg6THT8uL6tUsb3mqDhlB3vA8hT7o0flsKy/P9C5szav66ks7VzPMEQuoioMvfLKK/jxxx+xePFirF69GnfccQf+7//+DwcOHMDgwYPRr18/rFu3zlFtxYwZMzBs2DAMHz4cjRo1wsyZMxEbG4vPP/+81MeNGDECAwcORGJiosPaRnbau1eu6REZab5w0paaobLCkDvNKDOeVl8arbfk2LFDTo3X6QyrSqtVpYphB3Z7e4esCUPKlHtbw5AyRGbvYovFlbUStTJEdued6tbKKo/K6hly5hpDRFAZhr766ivMnj0b9957L7p164bFixfjjTfeQHx8PKZOnYqJEydi8uTJDmlofn4+du7cieRiMzWSk5Oxbds2i4/74osvcOzYMUyaNMmq18nLy0NOTo7JFzlBacXTgH09Q8ZbcRhzx54hS9PqFVoXUSsLpD76qOX1hKyhrDn09de2b89x5Yr8AhzbM6R1vZCirMUXvX0LDmOWwhBrhshFVIWhq1evoqbRX+01atTAzZs39QstPvjgg9hrbze5BRcvXkRhYSEii32wRUZGIsPCB8ORI0fw8ssvY9GiRfDzs65WfPr06QgLC9N/xfIvFOcorV4IMISh7GzD1NuyqOkZclLNm0VlFU8rtAxDv/4qP6D9/GTRtD169JBrA6Wny5lltlB6hapXtzxUCNgfhrRcY8iY8Q72xWco5uUZti3x9nohgMNk5HZUT61fvHix/va3336LihUrIup//0EXFRUhUMsZLmboivUaCCFK3AcAhYWFGDhwIKZMmYL6Zf21bWTChAnIzs7Wf51R/lIhxyptJhkg//MMDpbXre0dKisM1asng8C1a4aCWlexNgxpVTMkhNyoEpBrq9g7ZBQQILfnAGwfKrNmiAwwhKH0dLmpr1qO6hky3sF+3z7T723dKgu3o6KAZs20fV1PZK5nyJULLpLXUxWGpk6dijfeeAPt2rVDUlISBg0aZDL8tGbNGrRs2VLzRgJAtWrV4OvrW6IXKDMzs0RvESB7sXbs2IHRo0fDz88Pfn5+mDp1Kvbu3Qs/Pz9ssLC5ZGBgIEJDQ02+yMFycw1DVZbCkE6nfqisrDDk728IAa4cKlP2PwKc1zO0bp3sGQoMNAyV2UuZVbZ8uQyYalkbhqpXl+0WwrYQ66gwVNoO9sYbs3rzlHqF8v/q1auGlc+zsw3bujAMkZOpCkN33303/vzzT3Tt2hW33347Vq9ejbFjx+q///zzz+MXW7vIyxAQEIDWrVuXWOE6NTUVHTp0KHF8aGgo9u/fjz179ui/Ro4ciQYNGmDPnj1op3Rpk+vt2SP/Q4yONkyhN0dtEXVZYQhwjyLqkydlD0dQUMmVt4vTIgwZ9wqNGqXdB0+7drJ35Pp1GYjUsjYM6XS2D5Xl5Rke44hFDy3VDbFeyJQyTAbIQAQYeoWqVjX0AhM5iepFF5s1a4ZmLurmHT9+PAYNGoQ2bdogMTERc+bMwenTpzFy5EgAcojr7NmzWLhwIXx8fNCkSROTx0dERCAoKKjE/eRiZdULKbTuGQLco4haGSIzt1FkcVqEoRUrgJ075aKTEybY/jzF6XSyd+j11+VQmVJUbS1rwxAgw9CRI+rD0MmTMnhXrGhYyVpL5sLQ2bNyqxmdDrjnHu1f0xMFBsqe2Vu35FBZWBiLp8mlbFp00RJlMUZHGTBgAGbOnImpU6eiRYsW2LJlC1avXo24/021TU9PL3PNIXJDjghD164ZutzdvWdImVZvTW2bvWGosBB47TV5fexYOeSkJePtOdQOYakNQ4D6MGQ8ROaI4arbb5eXxjvYK71CbdvKXg+S5774lhysFyIX0jQMHT16FJ0dvJjYqFGjcPLkSeTl5WHnzp2466679N9bsGABNm3aZPGxkydPxp49exzaPrJBWcXTCjWrUCthISRE9gJY4k49Q2XVCwGGMJSba1tdzuLFwIEDQOXKwHPPqX98WeLj5To6QhhWtbaGEGVv0mrM3jCk9RpDiurVDTvYK7/XxltwkEHxLTm4xhC5kKZhiEi1q1cNYaCsMKSmZ0hZlLC0XiHAEIYyMgxr3DibmjBUsaJh2rna3qETJ4AXX5TXX3xRBiJHUIbH5s+X08mVD7nSXLli+FBUFlUsja1hyFHT6o0ZD5UVFADr18vbnFJvqviMMvYMkQupCkPh4eGlfhn30hBZZfdu2SsQG2t5cUSFmgJqa+qFAPkfstLj5KqhMjVhCLBtFeqUFNkbogRJ4wJWrfXrJ5csOHQIuPtuGW5SUkp/jDJEFhEBVKhQ9mtoMUzmKMZh6K+/5HBZlSqGITSSig+TsWaIXEhVAXVeXh6efvppNG3a1Oz3T506hSlTpmjSMPIS1tYLAep6hqwNQ4CsGzp3Toah9u3LPl5LV68awp2aMHTsmPU9Q2lpwFNPmS4sOWYM0LevYz54rl2TPSKKoiJgxAg5TGTp9dTUCwGmm7WWtkt8cc4OQ8oQ2T33yIBIBpaGyRiGyAVU/ets0aIFYmNjMWTIELPf37t3L8MQqWNLGMrKklPRAwIsH6smDDVsKAt+XVE3pBRPR0RYP2yltoj6yBHDWi4KZW0jR3zwHDlS8r6yXk9tGFLqSnJzZc+LNRuuFhQY6pIcGYaMd7CfP1/ex3qhkiwNk7FmiFxA1TBZr169cKWUuorw8HAMVjudlrybtcXTgJyJ4+8vr5cVBMral8yYK2eUqR0iA9SHoYSEkj0nvr6OCwTmlggo6/XUhqHgYMPUeGuHyk6floEoKKj09azsZbyDvfIBzzBUkvEwWU6OYb0hcxs1EzmY6l3rS9vwNDY2Fl988YXdjSIvceWKoRfBmjCkZhVqtT1DgGt7hlRsGaM6DMXEAMYbHPv6ArNnO244IiYGmDPHNICV9XpqwxCgvm5o+3bD48paz8leykrUgPz94gd8ScbDZEq9UJUqpe9LR+QgnE1GrrNrl7ysXRuoVs26x1hbRK22ZgiQdTh5eda1Qyu29AzZsj+ZspP8c8/J4DFsmPWPtcWwYcCffxpCR1m1WGqm1SvUhKGUFMN2IYcPl13Qba+bNw3XDx1y/Ot5IuNhMtYLkYsxDJHr7NwpL62pF1I4omeoRg35H3NRkaHA1lmcMUwmhJy1BwAPP+y8D5w2bYD77pPXZ8+2fJwQju0ZMldAPmKEdVP+bZGWBhj3kAvh2NfzVMbDZKwXIhdjGCLXUVYrT0iw/jHWhKGiIuvXGQLkcI4rhsqEMAyTOTIMpaXJonNfX8DZW9GMGCEvFy40rAhe3OXLhnoRa9YYUlgbhkorIHcEZ7+epzIeJmPPELkYwxC5RkoK8OOP8vrbb1s/jGDNKtSXL8s9jwDr959yRRH12bMyIPj5GVYttobxOkPFP3TNUXqFGjeWxb3O1LWrfG/Z2cCSJeaPUXqFIiPVbdBpbRjyhAJyb2Q8TMY1hsjFGIbI+ZRhC4WyDo01wwjW1AwpPSbh4XJDSGu4omdo61Z5GRtrmCVnDSXg3bpl2P+qNEoYatlSXfu04ONj6B2yNFRmyxAZYH0YiokBjNdGc1YBua+vc17PU5kbJuM5IhdhGCLns2cYwZphMjVDZApn9wylpAADB8rrJ06oK7ANDDSsq2PNUJkrwxAAPP64DHt//mloizF7w9C5c4aeQHNOnwb+/lteX7jQeQXkJ08CGzc65/U8kblhMtYMkYtoGoaGDBmCLl26aPmUVB7ZM2xhTRhSUzytUHqG/v3XuqEnWxUWyuHBJ5+0r6BXzZYcrg5DERHAgw/K6+Z6h2yZSQbITVEDA+V5PHvW8nHz5smfaZcuckaZs3ofYmKATp3Y22EJZ5ORG9E0DNWsWRNxagogyTvFxJh+MKsZRlDCUGam6ZYPxmwJQ3XqyN6L69e1mfWTliZ7BdLS5Nf8+XImV2Qk0KePaRAC1BfYWltEnZVlGEZSFgJ0BWWobNEiQ7G0wtaeIR8fQ0+CpaGyW7dkGAKAkSPVPT85lhKGcnMN+5NxPSZyEU03y5k2bZqWT0flWVaWvPzgA+Chh6z/i7B6dRmeCgtlIDK3krAtYcjfX/ZMHTwov5QhGFukpMiaKEs9TBUryv27jKktsLU2DO3ZIy/r1nXs5qxlSUqSM+YOHZKByDiY2BqGAPlzOnrUchhatUr2IkZEAPfeq/75yXGUMKQICwMqVXJNW8jradIzVFhYiD179uCyNcWcRBcuyA02AWDoUHVd476+hkUHLRVR2xKGAEPd0KpVtvcOKcXhxYNQy5bA66/LoulLl2RvhT0FttaGIVcPkSl0OkMAmjXL0DNm6xpDCqUnWvl9Kk4Zlhs2rPS97Mj5AgNNJziwXohcyKYwNHbsWKT8r+CzsLAQSUlJaNWqFWJjY7Fp0yYt20flkbLYYv36tvVWlFU3pGZfMmPKqsGffio/ZG1ZNdhccTgAzJgBTJkC3HGH7IWyt8DW2jCkrPLt6jAEAIMHyw+/vXtlMTUgg6HSS2ZLb1xpM8qOHQPWrZNB7MknbWszOZZx7xDrhciFbApDy5YtQ/PmzQEAq1atwokTJ/Dvv/9i7NixmDhxoqYNpHLIlpWnjVkbhtT0DKWlAT//bLitZrq/MXMLSFoaArOnwNbTeoYAOQNuwAB5XemxUXqFoqLUrTGkKC0MzZ0rL7t1U1+cTc5h/McQwxC5kE1h6OLFi4j633/Gq1evRr9+/VC/fn0MGzYM+/fv17SBVA4pO9W7Uxg6csT+omaF8Uw5R60xY83+ZLm5hu0+3CEMAYahsm++kWsk2TNEBlgOQ3l5smgdMBRvk/thzxC5CZvCUGRkJA4cOIDCwkKsWbMGXbt2BQBcv34dvkodBJEl9oah0lahvnULuHhRXlcThrRaNXjePBmq2rd37Boz1vQM7dsn2xIVpb5+ylHat5cLIN64AXz1le3T6hXGYcg4zK5YIWvToqOB3r3tazM5jnEYYs0QuZBNYWjo0KHo378/mjRpAp1Oh3vuuQcA8Mcff6Chsl4Llc14+rW3yMiQ71ens723orRVqC9ckB+Kvr5A1arWP6eyarBxIJoxQ91fqwUFhmnc//mPY9eYUcLNxYuWFxx0pyEyhXEh9ezZhjBka8+Q8gF67Rpw5YrhfmUY7skn5XYn5J44TEZuwqYwNHnyZMybNw9PPfUUfvvtNwT+b0aAr68vXn75ZU0bWG6lpMgi3S5dbC/W9URKvVDDhnKKuS1KGyZTekoiIgyztaylFDXXrStvF5/+XpaffpKL/1WvDtx/v7rHqlW1qnx/QsgAaI47hiEAePRRoEIF4MABYPlyeZ+tYSg4WJ5vwDBU9u+/wKZNMtgOH25va8mROExGbsKmMHTy5Ek89NBDGDduHGKMfoGHDBmCe7mWR9nS0uRfrMqsI1uLdT2RvcXTQOlhyJatOIzFxgKTJ8vrH30ka0+spfRGPPGE9Xui2crX17BHmaVVqN01DIWFGbYiUcKrrWEIKFk3NGeOvOzdmx+w7o5hiNyETWGoTp06uPPOOzF79mxcunRJ6zaVf1oW63oae+uFAEMYMrdru61rDBkbMED+x3z+PPDf/1r3mBMngDVr5HVnTeMurW7o1i1AmczgbmEIKLkadFCQ7c9lHIZu3AAWLJC3WTjt/pRhsgoV5LYcRC5iUxjasWMH2rdvjzfffBPR0dG49957sXTpUuSp+Svam9mzN5en0yIMRUbK81dQYCiWVmgRhvz9gbFj5fX337dur7K5c2XATU42DLM5Wmlh6OBBID9f/uXtjtPKW7c2LJgIAJ072z5UbByGli6Vs9Ti4uSUenJvymzH69e9q1yA3I5NYahVq1Z47733cPr0afz888+IiIjAiBEjEBERgSeeeELrNpY/MTHA6NGG246afu1uzp2TQ1s+Pvbtk+Xvb6gTKV5ErUUYAmTvTmioDBWrV5d+bH6+a6ZxlxaGlCGyFi1KzpJzB2lpptPh7RkqNg5DxoXTnNnq3tLSDDVjgHeVC5Dbset/SZ1Oh86dO2Pu3LlYv3496tSpgy+//FKrtpVvSs1EZKTjpl+7G6VXqHFj2S1uD0t1Q1qFodBQQ7B5993Sj/3hBzmkVqOG3ITVWawJQ+44RAZoO1SshKGNG4Ft2+TsMf5R5v68uVyA3I5dYejMmTN455130KJFC9x+++0ICQnBJ598olXbyrdq1eRlbm757xFSaFE8rSgrDKndisOc//xHfrBu2WLYPsIcpTdi+HDZa+UsnhyGtFrXCTAMtymF5PfdZ/j9IPel5e8AkZ1sCkNz5sxBUlIS4uPj8eWXX6J///44duwYtm7diqefflrrNpZPShi6ds2wJ1Z5p0W9kMLRPUMAULOmoQfvvffMH3P4MPDLL66Zxm0pDBUVGXarb9XKqU2ymrKukz2b1SqK72nGwmnPoOXvAJGdbFqN7I033sDDDz+MDz/8EC3sqf3wZmFh8h9/YSGQlSU/eMszITwvDAHA888DCxcC330HHD8O1Klj+n1lGnfPnrZtNGoPS2Ho+HE5MycwUK7n5K6GDZNFzkePyt4AWz8EV640va0s5EjuT6vfASI72RSGTp8+DV3x2VCkjk4ne4fOn5czosp7GEpLAzIzZQBs1sz+51O25DAuoL5+3TA9V6sw1LSp/M967Vrggw+Ajz82fO/mTddO47a0P5kyRNa0qXOH7WwRE2PfB2BaWslp+k8/DfTowQ9WT2Hv7wCRBmwaJmMQ0oiyXUTx6eHlkdIr1KSJbbuTF2euZ0ipGQkKMl3MzV4vvCAv58+XvXiK776Tt2Nj5YevsymBLydHBkGFu9cLaenIkZJLH7AIl4hUcsM5t15EqRvyhjCkZfE0UHoYiooquY6TPbp0kVPUr18HPv/ccL+rp3GHhhoWKzRehdqbwhCLcIlIAwxDrqSEIePehvJKy3ohwDQMKdNzta4XUuh0ht6hjz+Ww2P//AP8+qv84HXVsgg6neG9emsYYhEuEWmAYciVvKVnSOviacAQAvLzAWVLGEeFIQDo108Oh2VmAl99ZegVuvdeQ/2SKxQvok5Pl8HIx0eb2ixPoGywu3Gj96zZRUSaYhhyJW8JQ6dOyd4vf39Z1KuFoCAgPFxeV4bKHBmG/P2BcePk9WnTXLPitDnFw5DSK9Sggf0LW3qSmBigUyf2CBGRTVSHoUOHDmHy5Mm4++67UbduXdSoUQPNmjXDkCFD8PXXX3N/MjW8JQwpvUJNm2q7m3vxuiFHhiFAriMUHCx7H3Jz5X2nTjnmtaxlKQx5wxAZEZFGrA5Du3fvxj333IPmzZtjy5YtuP322zF27Fi88cYbeOyxxyCEwMSJExEdHY23336bocga3hKGtC6eVjg7DGVnl1wg8+mnXbuXEsMQEZHdrF5n6L777sMLL7yAJUuWIFwZnjBj+/bt+OCDD/D+++/jlVde0aSR5Za3TK3Xul5I4ewwVNpeSq4anmEYIiKym9U9Q0eOHMHo0aNLDUIAkJiYiG+//RbPP/+83Y0z57PPPkN8fDyCgoLQunVr/PrrrxaPXb58Oe655x5Ur14doaGhSExMxNq1ax3SLpt4w2wyRxRPK5QwpCy8qOW+ZOa44zRu4zCUnS1XnwYYhoiIVLA6DAUEBKh6YrXHW2PJkiUYO3YsJk6ciN27d6Njx47o0aMHTp8+bfb4LVu24J577sHq1auxc+dOdO7cGX369MFu5a9nV/OGYbLjx4ErV4CAAOC227R9bmUWlzK93tE9Q+44jds4DCn7kdWqZSguJyKiMqkqoN6wYQMaN26MHGXLAyPZ2dm47bbbSu2psdeMGTMwbNgwDB8+HI0aNcLMmTMRGxuLz40XwjMyc+ZMvPjii7j99tuRkJCAadOmISEhAatWrXJYG1VRwtD166YrCJcnSq9Q8+YyEGnJeJgsOxtQ6tQc1TMEuN80buMwtGuXvM5eISIiVVSFoZkzZ+LJJ59EqJmtDsLCwjBixAjMmDFDs8YZy8/Px86dO5GcnGxyf3JyMrZt22bVcxQVFeHq1aulDvXl5eUhJyfH5MthKlUy7B1VXofKHFU8DZiGIaVXKCxMm+0+SuNO07iV4JeXB2zaJK+76071RERuSlUY2rt3L7p3727x+8nJydipfPhp7OLFiygsLERksb/6IyMjkVF8o0oL3n//feTm5qJ///4Wj5k+fTrCwsL0X7GxsXa1u1TKZq1A+R0qc1S9EGA+DDlqiMxdBQXJAAgAv/wiL9kzRESkiqowdP78efiXsgu2n58fLly4YHejSlN8k1ghhFUbxy5evBiTJ0/GkiVLEBERYfG4CRMmIDs7W/915swZu9tcqvI8o6yoyDk9Q9evA4cPy+veFoYAw3tW1j5iGCIiUkVVGKpZsyb2799v8fv79u1DDeUDSmPVqlWDr69viV6gzMzMEr1FxS1ZsgTDhg3Dt99+i65du5Z6bGBgIEJDQ02+HKo8zyg7elTuqB4UBDRurP3zh4QYdqdXiuK9OQwB8vepZk3XtYWIyAOpCkM9e/bE66+/jpvFF54DcOPGDUyaNAm9e/fWrHHGAgIC0Lp1a6Smpprcn5qaig4dOlh83OLFi/H444/j66+/Rq9evRzSNruU52EypVeoRQvAz+olrdRRwjfDkNSypRx+JSIiq6n6hHr11VexfPly1K9fH6NHj0aDBg2g0+lw8OBBfPrppygsLMTEiRMd1VaMHz8egwYNQps2bZCYmIg5c+bg9OnTGDlyJAA5xHX27FksXLgQgAxCgwcPxocffoj27dvre5WCg4MRptRZuFp5DkOOrBdS1KgBHDoE7NsnbzMMua4dREQeSlUYioyMxLZt2/D0009jwoQJEP9bjVen06Fbt2747LPPyhyysseAAQOQlZWFqVOnIj09HU2aNMHq1asRFxcHAEhPTzdZc2j27NkoKCjAM888g2eeeUZ//5AhQ7BgwQKHtVMVhiH7KD1DN27IS28PQ7Vqua4dREQeSvXYRVxcHFavXo3Lly/j6NGjEEIgISEBVapUcUT7Shg1ahRGjRpl9nvFA84mZaqxOyuvYaiw0LDujTPCkMIbw5BSPA4AY8bIGi1Xr39ERORBbC7kqFKlCm6//XYt2+KdymsYOnwYuHYNqFABaNjQca+jrEKt8LYwlJYGGP8RUFQEjBgBdOvmHusgERF5AFUF1Ddu3MD06dPx8ssvI13ZHJPs44lT69PS5ArMpe3WrhRPt2xp2L7CEYr3DDly9Wl3VNrmsUREZBVVYWjYsGE4evQoqlatWuYUdbKSp02tnzlT1qV06QLExQEpKeaPc0a9EGAahnQ6oHp1x76eu3HHzWOJiDyMqjC0adMmjB8/Hi+88AKOHDmCzMxMR7XLexgPkxX/C9/drFsHjBtnaGdRETB8ODB2LLB1K3DrluHY336Tl3XqOLZNxmGoenXHTeF3V+64eSwRkYfRCWH9J/AjjzyCSpUqoX79+pg1axaOekFXfE5ODsLCwpCdne2YBRivXZN7lCnXQ0K0fw0tLF8ODBxo2AzVnNBQ2WMUEgIsWiTv8/GRH9aOKujNzgYqV5bXmzUD9u51zOu4u7Q0OTRWrx6DEBER1H1+q+oZmjdvHuLi4nD+/Hn8ouyDRPYJCQECA+V1d6wbEgJ44w3gwQfNByEfH6BPHyA8XK42/f33hiAEGAp6S6svskdoqCzSBryveNqYO20eS0TkYVSFoZCQEEycOBHvvvuufm0fspM7b9Z6/TowYADw+uvy9pgxcgjGeEhmzhxg5UogMxP46y/giSdKPo8jC3qN64SUHjYiIiIVVIUhchB3nFF25gxw553A0qWAvz8wdy7w4YfAU08BJ0/K2WQnTxqGv3x9ZbH0lCnOLehNSQFOnZLXly+3XNBNRERkgdVhaOTIkVbv4L5kyRIsMh4qodK5y4wyZcr8Dz8At98u9/uqXh345RdZKK0obUjGmQW9aWkynCmEcOyQHBERlUtWT72pXr06mjRpgg4dOqBv375o06YNoqOjERQUhMuXL+PAgQPYunUrvvnmG9SsWRNz5sxxZLvLF3cYJktJkcGiqMhwX7NmcghM7ZDosGFy0T9HF/QeOWLaXsAwJMfaGSIispLVYeiNN97As88+i5SUFMyaNQt///23yfcrVaqErl27Yt68eUhOTta8oeWaq8OQ0sNiHCx0OuDbb9UHIUVMjOMDibLGjnG7ucYOERGppGpRloiICEyYMAETJkzAlStXcOrUKdy4cQPVqlVD3bp1odPpHNXO8s3VYchcD4sQQHo60KCBa9pkDWVIbsQI2SPENXaIiMgGNq9QV7lyZVRW1nch+7g6DHlyD4uzhuSIiKjc4mwyd2BvGLJmr7DSxMTIafMKT+th4Ro7RERkB4Yhd6BMrbdlNllKiqzrKWuvsLIoCxd262Y6ZZ6IiKicYxhyB7b2DBUvfLZntefNm+XlgAHsYSEiIq+iKgydPn0aKrYyI2vZullraVPL1bhxA/jzT3n9rrvUPZaIiMjDqQpD8fHxuHDhgqPa4r2UMJSfLzdrtZZS+GzMlsLnP/6QO85HRzt+l3kiIiI3oyoMsVfIQSpUAIKD5XU1Q2UxMcDQoab32VL4vGWLvLzrLrm+EBERkRdhzZC7sLVuqHZtw/XAQGDgQPWvrYShpCT1jyUiIvJwqtcZmjdvHipWrFjqMWOMp2mTdapWlZujqp1RpmxSCgB5ebIQunt36x+fnw9s2yavs16IiIi8kOowNGvWLPgqm3CaodPpGIZsYWvPkBKGwsKA7GxgzRp1YWjnTllAXa0a0KiRutcmIiIqB1SHoR07diAiIsIRbfFu9oahQYOATz6RYUgNZYisY0fWCxERkVdSVTPEvcccyJYwJARw+rS8/sQTcibZoUNy0URrGRdPExEReSHOJnMXtoShzEzg5k3Zo3PbbUBiorx/7VrrHl9YCGzdKq8zDBERkZdSFYYmTZpUZvH0nj177GmP97IlDClDZNHRQECAoVbI2qGyffuAnBwgNBRo3tz61yUiIipHVIehCsoeVkays7Px2WefoXXr1mjTpo1mjfMqyv5ktoShuDh52a2bvPzlF7mIYlmUIbI775RDbERERF7IrnWGNmzYgMceeww1atTAlClTULt2bQ6l2UrpGVIztV4JQ8paQ61ayee5ehXYvr3sxyv7kXGIjIiIvJjqMJSWloY333wTdevWRd++fSGEwLJly3Du3DlMmTLFEW30DvYMkyk9Qz4+ht6hsobKhGDxNBEREVSGoZ49eyIhIQHbt2/H1KlTcf78eSxatAg9e/aEr68vZ5vZw5bNWouHIcD6uqGDB2UvVHAw0Lq1urYSERGVI6rWGVqzZg0GDhyIsWPHsjZIa0rNUEGBLGoOCyv7McoUeuMwlJwsL3fvBs6fByIjzT9W6RXq0EEWXxMREXkpVT1Dv/32G4KDg9GlSxc0aNAAU6dOxdGjRx3VNu8SHAyEhMjr1g6VmesZioiQtUMAsG6d5cdyiIyIiAiAyjCUmJiIuXPnIiMjAy+99BLWrVuHBg0aoH379vj4449x/vx5R7XTO6ipG7pyRfYgAUCtWqbfK2uojPVCREREejbNJqtQoQKeeOIJbN26FQcOHMBdd92FadOmoWvXrlq3z7soQ2XWzChTeoWqVTP0KCmUIuq1a+XCisUdPw6cPQv4+wPt2tneXiIionLArqn1ANCgQQO88847SEtLw/Lly9GrVy8t2uWd1PQMmRsiUyQmApUqyVC1a1fJ7yu9Qm3byuE5IiIiL2Z3GFL4+vrivvvuw8qVK7V6Su+jVRjy9weUXjpzW3NwiIyIiEhPszBEGtAqDAGlrzekhKGkJHXtIyIiKocYhtyJI8LQ9u3A5cuG+9PSZM2Qj4+cVk9EROTlGIbciZZhqHZtoGFDoKhI7lWm+PVXedmqlawrIiIi8nIMQ+7Eltlkyr5k5ihT7I3rhrgfGRERkQmPC0OfffYZ4uPjERQUhNatW+NXpafDgs2bN6N169YICgpCnTp1MGvWLCe11AbW9gzduAFkZsrrlnqGANO6IWWLDxZPExERmfCoMLRkyRKMHTsWEydOxO7du9GxY0f06NEDp0+fNnv8iRMn0LNnT3Ts2BG7d+/GK6+8gjFjxuC7775zcsutZG0YUnqFKlUCKle2fFxSEhAUJOuEDhyQAergQfm9O++0u7lERETlgUeFoRkzZmDYsGEYPnw4GjVqhJkzZyI2Nhaff/652eNnzZqFWrVqYebMmWjUqBGGDx+OJ554Au+9956TW24lJQxlZclaH0uM64VK2xw3ONgwY2zNGmDrVnm9aVPDkBwREZGX85gwlJ+fj507dyJZ2Yj0f5KTk7Ft2zazj9m+fXuJ47t164YdO3bg1q1bZh+Tl5eHnJwcky+nUQJKYSGQnW35uLKKp40Zr0bNITIiIqISPCYMXbx4EYWFhYgstgt7ZGQkMjIyzD4mIyPD7PEFBQW4aGEoavr06QgLC9N/xcbGavMGrBEYaJjhVdpQmZowpBRRb95sKKRmGCIiItLzmDCk0BUbFhJClLivrOPN3a+YMGECsrOz9V9nzpyxs8UqGQ+VWaImDDVsKDdyzc8H/v1X3texo31tJCIiKkc8JgxVq1YNvr6+JXqBMjMzS/T+KKKioswe7+fnh6oWamYCAwMRGhpq8uVUSru06hnS6Qy9Q4Ccil+jhs3NIyIiKm88JgwFBASgdevWSE1NNbk/NTUVHSyspJyYmFji+HXr1qFNmzbw9/d3WFvtYs2MMjVhCAB8fU0fm5JiW9uIiIjKIY8JQwAwfvx4zJs3D/Pnz8fBgwcxbtw4nD59GiNHjgQgh7gGDx6sP37kyJE4deoUxo8fj4MHD2L+/PlISUnB888/76q3ULaywtCtW8DZs/K6NWEoLQ2YPdtwWwhgxAh5PxEREcHP1Q1QY8CAAcjKysLUqVORnp6OJk2aYPXq1Yj7XyhIT083WXMoPj4eq1evxrhx4/Dpp58iOjoaH330ER588EFXvYWylRWGzp6V0+4DAgALw4MmjhwpOU2/sBA4ehSIibGvrUREROWAR4UhABg1ahRGjRpl9nsLFiwocV9SUhJ27drl4FZpqKwwpAyR1aolN1stS0KCPM44EPn6AvXq2ddOIiKicsKjhsm8QlmzyazZk8xYTAwwZ46hbsjXVw6bsVeIiIgIgAf2DJV7Zc0mO3lSXlpbPA0Aw4bJxRePHpU9QgxCREREegxD7sbaYTI1YQiQAYghiIiIqAQOk7kbR4UhIiIiMothyN0oYejSJTnrqziGISIiIk0xDLkbpWaoqAi4csX0e0VFgLJ0AMMQERGRJhiG3I2/PxAWJq8XHyo7f17uMebjA9Ss6fy2ERERlUMMQ+7I0vR6ZYisZk0ZmoiIiMhuDEPuyNL0etYLERERaY5hyB1ZmlHGMERERKQ5hiF3xDBERETkNAxD7qisMGTtVhxERERUJoYhd2QpDNmyFQcRERGVimHIHZmbTSYEh8mIiIgcgGHIHZmbTXb5MnDtmrxeq5bz20RERFROMQy5I3PDZEqvUEQEEBzs/DYRERGVUwxD7qi0MMQhMiIiIk0xDLkjJQxdvgwUFMjrDENEREQOwTDkjsLD5aUQMhABDENEREQOwjDkjvz8gCpV5HVlRhnDEBERkUMwDLmr4nVDDENEREQOwTDkropPr2cYIiIicgiGIXdl3DOUm2sIRQxDREREmmIYclfGYUjpFQoLAypXdlmTiIiIyiOGIXdlLgyxV4iIiEhzDEPuynh/MoYhIiIih2EYclfsGSIiInIKhiF3ZTybjGGIiIjIYfxc3QCywLhnyOd/mZVhiIiISHMMQ+7KOAzduCGvMwwRERFpjmHIXSlh6MoVIDtbXmcYIiIi0hxrhtxVlSqATievCwEEBQEREa5tExERUTnEMOSufH0Nu9cDQK1ahnBEREREmmEYcmfKUBnAITIiIiIHYRhyZ8r0egCoXdtlzSAiIirPGIbcGXuGiIiIHI5hyJ0xDBERETkcw5A7YxgiIiJyOIYhd2YchgICXNcOIiKicsxjwtDly5cxaNAghIWFISwsDIMGDcKVK1csHn/r1i289NJLaNq0KUJCQhAdHY3Bgwfj3Llzzmu0vQ4cMFzv0AFISXFdW4iIiMopjwlDAwcOxJ49e7BmzRqsWbMGe/bswaBBgywef/36dezatQuvvfYadu3aheXLl+Pw4cPo27evE1tth7Q04MsvDbeLioARI+T9REREpBmP2I7j4MGDWLNmDX7//Xe0a9cOADB37lwkJibi0KFDaNCgQYnHhIWFITU11eS+jz/+GG3btsXp06dRq1Ytp7TdZkeOyJWnjRUWAkePAjExrmkTERFROeQRPUPbt29HWFiYPggBQPv27REWFoZt27ZZ/TzZ2dnQ6XSoXLmyxWPy8vKQk5Nj8uUSCQmG3eoVvr5AvXquaQ8REVE55RFhKCMjAxFm9uWKiIhARkaGVc9x8+ZNvPzyyxg4cCBCQ0MtHjd9+nR9XVJYWBhiY2NtbrddYmKAOXNkAALk5ezZ7BUiIiLSmEvD0OTJk6HT6Ur92rFjBwBAZ2ZfLiGE2fuLu3XrFh5++GEUFRXhs88+K/XYCRMmIDs7W/915swZ296cFoYNA06eBDZulJfDhrmuLUREROWUS2uGRo8ejYcffrjUY2rXro19+/bh/PnzJb534cIFREZGlvr4W7duoX///jhx4gQ2bNhQaq8QAAQGBiIwMLDsxjtLTAx7g4iIiBzIpWGoWrVqqGa8lo4FiYmJyM7Oxp9//om2bdsCAP744w9kZ2ejQ4cOFh+nBKEjR45g48aNqGq81xcRERERPKRmqFGjRujevTuefPJJ/P777/j999/x5JNPonfv3iYzyRo2bIgVK1YAAAoKCvDQQw9hx44dWLRoEQoLC5GRkYGMjAzk5+e76q0QERGRm/GIMAQAixYtQtOmTZGcnIzk5GQ0a9YMX331lckxhw4dQnZ2NgAgLS0NK1euRFpaGlq0aIEaNWrov9TMQCMiIqLyTSdE8cVsyFhOTg7CwsKQnZ1dZr0RERERuQc1n98e0zNERERE5AgMQ0REROTVGIaIiIjIqzEMERERkVdjGCIiIiKvxjBEREREXo1hiIiIiLyaS7fj8ATKMkw5OTkubgkRERFZS/nctmY5RYahMly9ehUAEBsb6+KWEBERkVpXr15FWFhYqcdwBeoyFBUV4dy5c6hUqRJ0Op2rm1Ou5OTkIDY2FmfOnOHq3k7A8+1cPN/OxfPtXJ5wvoUQuHr1KqKjo+HjU3pVEHuGyuDj44OYmBhXN6NcCw0Nddt/TOURz7dz8Xw7F8+3c7n7+S6rR0jBAmoiIiLyagxDRERE5NUYhshlAgMDMWnSJAQGBrq6KV6B59u5eL6di+fbucrb+WYBNREREXk19gwRERGRV2MYIiIiIq/GMERERERejWGIiIiIvBrDENlly5Yt6NOnD6Kjo6HT6fD999+bfP/8+fN4/PHHER0djQoVKqB79+44cuSIyTEZGRkYNGgQoqKiEBISglatWmHZsmUmx1y+fBmDBg1CWFgYwsLCMGjQIFy5csXB7879aHG+jx07hvvvvx/Vq1dHaGgo+vfvj/Pnz5scw/MNTJ8+HbfffjsqVaqEiIgI3HfffTh06JDJMUIITJ48GdHR0QgODkanTp3wzz//mByTl5eHZ599FtWqVUNISAj69u2LtLQ0k2N4vrU733PmzEGnTp0QGhoKnU5n9jzyfGtzvi9duoRnn30WDRo0QIUKFVCrVi2MGTMG2dnZJs/jCeebYYjskpubi+bNm+OTTz4p8T0hBO677z4cP34cP/zwA3bv3o24uDh07doVubm5+uMGDRqEQ4cOYeXKldi/fz8eeOABDBgwALt379YfM3DgQOzZswdr1qzBmjVrsGfPHgwaNMgp79Gd2Hu+c3NzkZycDJ1Ohw0bNuC3335Dfn4++vTpg6KiIv1z8XwDmzdvxjPPPIPff/8dqampKCgoQHJyssnv7jvvvIMZM2bgk08+wV9//YWoqCjcc889+j0NAWDs2LFYsWIFvvnmG2zduhXXrl1D7969UVhYqD+G51u78339+nV0794dr7zyisXX4vnW5nyfO3cO586dw3vvvYf9+/djwYIFWLNmDYYNG2byWh5xvgWRRgCIFStW6G8fOnRIABB///23/r6CggIRHh4u5s6dq78vJCRELFy40OS5wsPDxbx584QQQhw4cEAAEL///rv++9u3bxcAxL///uugd+P+bDnfa9euFT4+PiI7O1t/zKVLlwQAkZqaKoTg+bYkMzNTABCbN28WQghRVFQkoqKixP/93//pj7l586YICwsTs2bNEkIIceXKFeHv7y+++eYb/TFnz54VPj4+Ys2aNUIInm9LbDnfxjZu3CgAiMuXL5vcz/Ntnr3nW/Htt9+KgIAAcevWLSGE55xv9gyRw+Tl5QEAgoKC9Pf5+voiICAAW7du1d935513YsmSJbh06RKKiorwzTffIC8vD506dQIAbN++HWFhYWjXrp3+Me3bt0dYWBi2bdvmnDfjAaw533l5edDpdCYLpQUFBcHHx0d/DM+3eUrXf3h4OADgxIkTyMjIQHJysv6YwMBAJCUl6c/Tzp07cevWLZNjoqOj0aRJE/0xPN/m2XK+rcHzbZ5W5zs7OxuhoaHw85Nbn3rK+WYYIodp2LAh4uLiMGHCBFy+fBn5+fn4v//7P2RkZCA9PV1/3JIlS1BQUICqVasiMDAQI0aMwIoVK1C3bl0AsqYoIiKixPNHREQgIyPDae/H3Vlzvtu3b4+QkBC89NJLuH79OnJzc/HCCy+gqKhIfwzPd0lCCIwfPx533nknmjRpAgD6cxEZGWlybGRkpP57GRkZCAgIQJUqVUo9hufblK3n2xo83yVpdb6zsrLwxhtvYMSIEfr7POV8MwyRw/j7++O7777D4cOHER4ejgoVKmDTpk3o0aMHfH199ce9+uqruHz5MtavX48dO3Zg/Pjx6NevH/bv368/RqfTlXh+IYTZ+72VNee7evXqWLp0KVatWoWKFSsiLCwM2dnZaNWqlcnPhOfb1OjRo7Fv3z4sXry4xPeKnxNrzlPxY3i+TWl9vst6Dlufp7zQ4nzn5OSgV69eaNy4MSZNmlTqc5T2PK7i5+oGUPnWunVr7NmzB9nZ2cjPz0f16tXRrl07tGnTBoCc2fTJJ5/g77//xm233QYAaN68OX799Vd8+umnmDVrFqKiokrMdgKACxculPirxduVdb4BIDk5GceOHcPFixfh5+eHypUrIyoqCvHx8QDA813Ms88+i5UrV2LLli2IiYnR3x8VFQVA/uVbo0YN/f2ZmZn68xQVFYX8/HxcvnzZpHcoMzMTHTp00B/D821gz/m2Bs+3KS3O99WrV9G9e3dUrFgRK1asgL+/v8nzeML5Zs8QOUVYWBiqV6+OI0eOYMeOHbj33nsByJkfAODjY/qr6Ovrq5/dlJiYiOzsbPz555/67//xxx/Izs7Wf6CQKUvn21i1atVQuXJlbNiwAZmZmejbty8Anm+FEAKjR4/G8uXLsWHDBn1YVMTHxyMqKgqpqan6+/Lz87F582b9eWrdujX8/f1NjklPT8fff/+tP4bnW9LifFuD51vS6nzn5OQgOTkZAQEBWLlypUnNIuBB59sFRdtUjly9elXs3r1b7N69WwAQM2bMELt37xanTp0SQsiZBRs3bhTHjh0T33//vYiLixMPPPCA/vH5+fmiXr16omPHjuKPP/4QR48eFe+9957Q6XTip59+0h/XvXt30axZM7F9+3axfft20bRpU9G7d2+nv19Xs/d8CyHE/Pnzxfbt28XRo0fFV199JcLDw8X48eNNjuH5FuLpp58WYWFhYtOmTSI9PV3/df36df0x//d//yfCwsLE8uXLxf79+8UjjzwiatSoIXJycvTHjBw5UsTExIj169eLXbt2iS5duojmzZuLgoIC/TE839qd7/T0dLF7924xd+5cAUBs2bJF7N69W2RlZemP4fnW5nzn5OSIdu3aiaZNm4qjR4+aPI+n/X4zDJFdlOmrxb+GDBkihBDiww8/FDExMcLf31/UqlVLvPrqqyIvL8/kOQ4fPiweeOABERERISpUqCCaNWtWYqp9VlaWePTRR0WlSpVEpUqVxKOPPlpiyqw30OJ8v/TSSyIyMlL4+/uLhIQE8f7774uioiKTY3i+hdnzDEB88cUX+mOKiorEpEmTRFRUlAgMDBR33XWX2L9/v8nz3LhxQ4wePVqEh4eL4OBg0bt3b3H69GmTY3i+tTvfkyZNKvN5eL61Od+W/j8CIE6cOKE/zhPOt04IIRzV60RERETk7lgzRERERF6NYYiIiIi8GsMQEREReTWGISIiIvJqDENERETk1RiGiIiIyKsxDBEREZFXYxgiIiIir8YwRERERF6NYYiIyAaFhYX6zYSJyLMxDBGRx1u4cCGqVq2KvLw8k/sffPBBDB48GACwatUqtG7dGkFBQahTpw6mTJmCgoIC/bEzZsxA06ZNERISgtjYWIwaNQrXrl3Tf3/BggWoXLkyfvzxRzRu3BiBgYE4deqUc94gETkUwxARebx+/fqhsLAQK1eu1N938eJF/Pjjjxg6dCjWrl2Lxx57DGPGjMGBAwcwe/ZsLFiwAG+99Zb+eB8fH3z00Uf4+++/8eWXX2LDhg148cUXTV7n+vXrmD59OubNm4d//vkHERERTnuPROQ43KiViMqFUaNG4eTJk1i9ejUA4MMPP8RHH32Eo0ePIikpCT169MCECRP0x//3v//Fiy++iHPnzpl9vqVLl+Lpp5/GxYsXAcieoaFDh2LPnj1o3ry5498QETkNwxARlQu7d+/G7bffjlOnTqFmzZpo0aIFHnzwQbz22msICQlBUVERfH199ccXFhbi5s2byM3NRYUKFbBx40ZMmzYNBw4cQE5ODgoKCnDz5k1cu3YNISEhWLBgAUaMGIGbN29Cp9O58J0Skdb8XN0AIiIttGzZEs2bN8fChQvRrVs37N+/H6tWrQIAFBUVYcqUKXjggQdKPC4oKAinTp1Cz549MXLkSLzxxhsIDw/H1q1bMWzYMNy6dUt/bHBwMIMQUTnEMERE5cbw4cPxwQcf4OzZs+jatStiY2MBAK1atcKhQ4dQr149s4/bsWMHCgoK8P7778PHR5ZSfvvtt05rNxG5FsMQEZUbjz76KJ5//nnMnTsXCxcu1N//+uuvo3fv3oiNjUW/fv3g4+ODffv2Yf/+/XjzzTdRt25dFBQU4OOPP0afPn3w22+/YdasWS58J0TkTJxNRkTlRmhoKB588EFUrFgR9913n/7+bt264ccff0Rqaipuv/12tG/fHjNmzEBcXBwAoEWLFpgxYwbefvttNGnSBIsWLcL06dNd9C6IyNlYQE1E5co999yDRo0a4aOPPnJ1U4jIQzAMEVG5cOnSJaxbtw6PPvooDhw4gAYNGri6SUTkIVgzRETlQqtWrXD58mW8/fbbDEJEpAp7hoiIiMirsYCaiIiIvBrDEBEREXk1hiEiIiLyagxDRERE5NUYhoiIiMirMQwRERGRV2MYIiIiIq/GMERERERejWGIiIiIvNr/A7zdO1RHyg5pAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'Global average temperature change')"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Is this a big change?  For comparison, in [the most recent ice age](https://en.wikipedia.org/wiki/Last_Glacial_Maximum), the global average temperature was [about 6° C colder](https://www.smithsonianmag.com/smart-news/ice-age-temperature-science-how-cold-180975674/) than it is now … but that change took thousands of years.\n",
    "\n",
    "So over my lifetime the temperature has changed by 1/6 of an ice age, [warming > 10× faster than after the ice age](https://royalsociety.org/topics-policy/projects/climate-change-evidence-causes/question-6/), and in fact changing faster than it has [for millions of years](https://news.stanford.edu/news/2013/august/climate-change-speed-080113.html).\n",
    "\n",
    "![xkcd: Thickness of Ice Sheets](https://imgs.xkcd.com/comics/ice_sheets.png)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Naive slope estimation: Pick two data points"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "If you would like to **estimate the slope** (the rate of **change of temperature per year**), a **naive** way would be to **pick two points** and draw a straight line through them, but this would be a pretty poor approach because the data is so noisy.\n",
    "\n",
    "You will get **wildly varying slopes** depending on which years you picked, especially for years that are close together:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "plot(year, ΔT, \"r.-\")\n",
    "xlabel(\"year\")\n",
    "ylabel(\"ΔT (°C) vs. 1901–2000 baseline\")\n",
    "title(\"Global average temperature change\")\n",
    "\n",
    "for (i,j,c) in ((1,50,\"k\"), (26,34,\"b\"), (25,35,\"g\"))\n",
    "    slope = (ΔT[j] - ΔT[i]) / (year[j] - year[i])\n",
    "    plot(year[[i,j]], ΔT[[i,j]], \"$(c)o\")\n",
    "    plot(year[[begin,end]], ΔT[i] .+ (year[[begin,end]] .- year[i]) .* slope, \"$c-\")\n",
    "end\n",
    "\n",
    "ylim(-0.2, 1.2)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(-0.2, 1.2)"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Even using the first and last points is not that great of an estimate unless the timespan is extremely long (but over a longer timescale the change is not linear … in the last century it has accelerated enormously)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Least-square fitting\n",
    "\n",
    "Instead, a much more reliable approach is to look at *all* the data simultaneously.\n",
    "\n",
    "We can't draw a single line that goes through all of the points, but we can try to minimize some *average* error between the fit and *all* of the points.   The most common approach is to minimize the average |error|², which is called a [least squares fit](https://en.wikipedia.org/wiki/Least_squares) or, in the particular case of fitting to a *line*, [linear regression](https://en.wikipedia.org/wiki/Linear_regression):\n",
    "\n",
    "For example, if we want to fit to the linear model\n",
    "$$\n",
    "\\mathrm{model}(\\mathrm{year}) = \\Delta T = x_1 + x_2 (\\mathrm{year} - 1973)\n",
    "$$\n",
    "where $x_1$ is the intercept and $x_2$ is the slope, then sum of the squares of errors for $m$ data points is:\n",
    "$$\n",
    "\\mathrm{SSE} = \\sum_{k=1}^m \\big[ \\Delta T_k - \\underbrace{\\mathrm{model}(\\mathrm{year}_k)}_{\\mbox{row }k\\mbox{ of }Ax} \\big]^2\n",
    "$$\n",
    "\n",
    "### Matrix formulation\n",
    "\n",
    "A key fact is that **this model depends linearly** on the **unknown x** parameters.  And so we can write it in terms of matrix and vector algebra.\n",
    "\n",
    "In matrix form, we obtain:\n",
    "$$\n",
    "\\mathrm{SSE} = \\Vert b - Ax \\Vert^2\n",
    "$$\n",
    "where\n",
    "$$\n",
    "A = \\begin{pmatrix} 1 & \\mathrm{year}_1 - 1973 \\\\ 1 & \\mathrm{year}_2 - 1973 \\\\ \\vdots & \\vdots \\\\ 1 & \\mathrm{year}_m - 1973 \\end{pmatrix}, \n",
    "\\qquad x = \\begin{pmatrix} x_1 \\\\ x_2 \\end{pmatrix}, \\qquad b = \\begin{pmatrix} \\Delta T_1 \\\\ \\Delta T_2 \\\\ \\vdots \\Delta T_m \\end{pmatrix} \\, .\n",
    "$$\n",
    "As we've seen in class, the minimum of $\\Vert b - Ax \\Vert^2$ is achieved by **orthogonal projection** of $b$ onto $C(A)$, corresponding to $\\hat{x}$ solving the \"normal equations\"\n",
    "$$\n",
    "A^T A \\hat{x} = A^T b\n",
    "$$\n",
    "or simply by `A \\ b` in Julia:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "b = ΔT\n",
    "A = [ones(length(year)) year.-1973]\n",
    "\n",
    "x̂ = A \\ b"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.08468235294117633\n",
       " 0.01638847539015606"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "# Alternatively, the normal equations solution:\n",
    "(A'A) \\ A'b"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.08468235294117676\n",
       " 0.016388475390156053"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's plot it:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "using PyPlot\n",
    "plot(year, ΔT, \"r.-\")\n",
    "xlabel(\"year\")\n",
    "ylabel(\"ΔT (°C) vs. 1901–2000 baseline\")\n",
    "title(\"Global average temperature change: Linear fit\")\n",
    "\n",
    "plot(year, A * x̂, \"k-\")\n",
    "legend([\"data\", \"fit: slope $(round(x̂[2], sigdigits=2)) °C/year\"])"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x7fa7e579eca0>"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "It's obvious by eye that this fit line is a better description of the overall trend than any two data points.\n",
    "\n",
    "More precisely, if the data noise is uncorrelated, then in a certain statistical sense a least-squares estimate is optimal, as described by the [Gauss–Markov theorem](https://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [],
   "outputs": [],
   "metadata": {}
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.7.2",
   "language": "julia",
   "name": "julia-1.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.7.2"
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 },
 "nbformat": 4,
 "nbformat_minor": 5
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